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Publication

 

In this page I only list the papers that is published or has been submitted to a journals, the list of the preprints can be found in my CV.

Also you can find my papers in  arXiv or  inSPIRE or Google Scholar

 

26)  21 cm power spectrum and ionization bias as a probe of long mode modulated non Gaussian sky

Shahram Khosravi, Amirabbas Ghazizadeh, Shant Baghram,  https://arxiv.org/abs/1812.11150 submitted to MNRAS

 The observed hemispherical asymmetry in cosmic microwave background radiation can be explained by long mode modulation. In this work we study the prospect of the detection of this effect in 21cm brightness temperature fluctuations angular power spectrum. For this task, we study the effect of the neutral Hydrogen distribution on the angular power spectrum. This is done by formulating the bias parameter of ionized fraction to the underlying matter distribution. We also discuss the possibility that the long mode modulation is companied with a primordial non-Gaussianity of local type. In this case we obtain the angular power spectrum with two effects of primordial non-Gaussianity and long mode modulation. Finally, we show that the primordial non-Gaussianity enhances the long mode modulated power of 21cm via the non-Gaussian scale dependent bias up to four order of magnitude. Accordingly the future observations of 21cm cosmology such as square kilometer array are capable of detection of large scale anomalies in initial condition of early Universe.

25)  Cosmological Filaments in the light of Excursion Set of Saddle Points

Mohammad Ansari Fard, Sina Taamoli, Shant Baghram , https://arxiv.org/abs/1811.12398,  submitted to MNRAS

 The universe in large scales is structured as a network, called cosmic web. Filaments are one of the structural components of this web, which can be introduced as a novel probe to study the formation and evolution of structures and as a probe to study the cosmological models and even to address the missing baryon problem. The aim of this work is to introduce an analytical framework to study the statistics of filaments. In this direction, we have a plan to present an approach to obtain the length to mass relation of filaments and the number density of filaments per length and mass. For this objective, we model filaments as collapsed objects which have an extension in one direction, accordingly we use the ellipsoidal collapse to study the evolution of an over-dense region via gravitational instability. In this context, the critical density of filament formation is obtained which will be a crucial parameter for number density count. Also, we find that the nonlinear density of filaments in the epoch of formation is almost mass independent and is in order of 30. A fitting function is presented for length-mass relation. For the statistics of filaments, we propose a novel framework which we named it as excursion set of saddle points. In this approach, we count the saddle points of the density field Hessian matrix, and relate it to the count of filaments. In addition, we addressed the filament in filament problem with up-crossing approximation.

 

24)  The Excursion set approach: Stratonovich approximation and Cholesky decomposition

Farnik Nikakhtar, Mohammadreza Ayromlou, Shant Baghram, Sohrab Rahvar, M. Reza Rahimi Tabar, Ravi K. Sheth,  Mon.Not.Roy.Astron.Soc. 478 (2018) no.4, 5296-5300

The excursion set approach is a framework for estimating how the number density of nonlinear structures in the cosmic web depends on the expansion history of the universe and the nature of gravity. A key part of the approach is the estimation of the first crossing distribution of a suitably chosen barrier by random walks having correlated steps: The shape of the barrier is determined by the physics of nonlinear collapse, and the correlations between steps by the nature of the initial density fluctuation field. We describe analytic and numerical methods for calculating such first up-crossing distributions. While the exact solution can be written formally as an infinite series, we show how to approximate it efficiently using the Stratonovich approximation. We demonstrate its accuracy using Monte-Carlo realizations of the walks, which we generate using a novel Cholesky-decomposition based algorithm, which is significantly faster than the algorithm that is currently in the literature.

 

23)  üΛCDM: H0 tension as a hint for Über-Gravity

Nima Khosravi, Shant Baghram, Niayesh Afshordi, Natacha Altamirano,  arXiv:1710.09366,  submitted to Physical Review D

 We propose a cosmological model, üΛCDM, based on über-gravity, which is a canonical ensemble average of many theories of gravity. In this model, we have a sharp transition from (a purely) ΛCDM era to a phase in which the Ricci scalar is a constant. This transition occurs when the Ricci scalar reaches a critical scale or alternatively at a transition redshift ...

22)  Late time sky as a probe of steps and oscillations in primordial Universe

Mohammad Ansari Fard, Shant Baghram  arXiv:1709.05323 - Accepted for Publication in JCAP

We The standard model of cosmology with nearly Gaussian, isotropic, scale invariant and adiabatic initial conditions describes the cosmological observations well. However, the study of any deviation from the mentioned conditions will open up a new horizon to the physics of early universe. In this work, we study the effect of the oscillatory and step-like features in potentials of inflationary models in late time large scale structure observations. Mainly we study the matter power spectrum, number density of the structures, dark matter halo bias and specifically CMB lensing. We show that the oscillatory models can introduce some degeneracy with late time effects on BAO scale. We also conclude that high frequency oscillatory models which are favored by Planck data do not have significant effect on the non linear structure formation. Finally we show that inflationary models with step functions which deviates from the standard model in small scales l≤1Mpc can be constrained by future experiments via CMB lensing. We propose the idea that CMB lensing is a bias independent observation which can be used as a small scale physics probe due to distribution of the lenses in low redshifts. Meantime this model can alter the prediction of the cosmological model for the number density of small structures and can be used as a probable explanation for galactic scale crisis of ΛCDM.

 

21)  Measuring the baryon fraction in cluster of galaxies with Kinematic Sunyeav Zeldovich and a Standard Candle

Shant Baghram  arXiv:1703.02021 - Accepted for publication in JCAP

We propose a new method to use the Kinetic Sunyaev-Zeldovich for measuring the baryon fraction in cluster of galaxies. In this proposal we need a configuration that a supernova Type Ia resides in a brightest central galaxy of low redshift cluster of galaxy. We show that this supernova Type Ia can be used to measure the bulk velocity of a galaxy cluster in low redshifts where the main contribution to the standard candles distance modulus deviation from background prediction comes from peculiar velocity of the host. Then we argue that by the knowledge of the bulk flow of the galaxy cluster and the Cosmic microwave background photons temperature change due to kSZ, we can constrain the baryon fraction of galaxy cluster. The probability of this configuration for clusters in low redshift z<0.15z<0.15 is obtained. We estimate that in a conservative parameter estimation the large synoptic survey telescope can find ∼30∼30 galaxy clusters in low redshift with a bright central galaxy which host a type Ia Supernova. Finally, we show that the improving of the distance modulus measurement in future surveys is crucial to detect the baryon fraction of cluster with the proposed method.

 

20)  Supernovae anisotropy power spectrum

Hoda Ghodsi, Shant Baghram  and Farhang Habibi:   JCAP 10(2017)017 - arXiv:1609.08012

We contribute another anisotropy study to this field of research using Supernovae Type Ia (SNe Ia). In this work, we utilise the power spectrum calculation method and apply it to both the current SNe Ia data and simulation. Our simulations are constructed with the characteristics of the upcoming survey of the Large Synoptic Survey Telescope (LSST), which shall bring us the largest SNe Ia collection to date. We make predictions for the amplitude of a possible dipole anisotropy or anisotropy in higher multipole moments that would be detectable by the LSST.

 

19)  Matrix Formalism of Excursion Set Theory: A new approach to statistics of dark matter halo counting

Farnik Nikakhtar and Shant Baghram :  arXiv:1606.06666,  Phys. Rev. D 96, 043524 (2017)

Excursion Set Theory (EST) is an analytical framework to study the large scale structure of the Universe. EST introduces a procedure to calculate the number density of structures by relating the non-linear structures to cosmological linear perturbation theory. In this work, we introduce a novel approach to re-formulate the EST in Matrix Formalism. It is proposed that the matrix representation of EST will facilitate the the calculations in framework of the large scale structure observables. The method is to discretize the two dimensional plane of variance and density contrast of EST, where the trajectories for each point in the Universe lived there. The probability of having a density contrast in a chosen variance is represented by a probability ket. Naturally the concept of the transition matrix pops up to define the trajectories in EST. We show that in the case of Markovianity of the process, the probability ket, at a specific variance can be constructed by knowing the transition matrix and the initial probability ket. We should note that, in a specific case of Gaussian transitions, the Gaussian profile of density contrast is preserved. In this formalism we define the probability transition rate which is used to obtain the first up-crossing of trajectories and the number count of the structures. The continues limit of the formalism is discussed and the known Fokker-Planck dispersion equation of EST is recovered. Finally we claim and discuss that the Matrix Formalism of EST could be a powerful complimentary approach in non-linear structure formation studies.

18)  Lensing as a Probe of Early Universe: from CMB to Galaxies

Farbod Hassani, Shant Baghram, Hassan Firouzjahi : arXiv:1511.05534 ,  JCAP 05 (2016) 044.

The Cosmic Microwave Background (CMB) radiation lensing is a promising tool to study the physics of early universe. In this work we probe the imprints of deviations from isotropy and scale invariance of primordial curvature perturbation power spectrum on CMB lensing potential and convergence. Specifically, we consider a scale-dependent hemispherical asymmetry in primordial power spectrum. We show that the CMB lensing potential and convergence and also the cross-correlation of the CMB lensing and late time galaxy convergence can probe the amplitude and the scale dependence of the dipole modulation. As another example, we consider a primordial power spectrum with local feature. We show that the CMB lensing and the cross-correlation of the CMB lensing and galaxy lensing can probe the amplitude and the shape of the local feature. We show that the cross correlation of CMB lensing convergence and galaxy lensing is capable to probe the effects of local features in power spectrum on smaller scales than the CMB lensing.

17)  ISW-Galaxy Cross Correlation:A probe of Dark Energy clustering and distribution of Dark Matter tracers

Shahram Khosravi, Amir Mollazadeh, Shant Baghram : arXiv:1510.01720,  JCAP 09 (2016) 003.

 

16)  Peculiar velocity measurement in a clumpy universe

Farhang Habibi, Shant Baghram, Saeed Tavasoli,  Accepted for publication in International Journal of Modern Physics D ,   arXiv:1412.8457

At low redshifts, deviations of the measured luminosity distance from the background FRW universe can be attributed to peculiar velocities of galaxies. Via observing the cosmic standard candles, this is one of the conventional ways to estimate peculiar velocities. However, at intermediate redshifts (z>0.5), deviations from the background FRW model are not uniquely governed by peculiar velocities. Luminosity distances are modified by gravitational lensing which affects the light trajectories. Hence using the conventional peculiar velocity method will result in an overestimate of the measured peculiar velocities at intermediate redshifts. Here we quantify this effect and show that although present data are still incapable of extracting any lensing effect on distance measurement and peculiar velocity estimation, this effect will however be significant for future large-scale structure surveys

15) Unraveling the nature of Gravity through our clumpy Universe

Shant Baghram, Saeed Tavasoli, Farhang Habibi, Roya Mohayaee, Joseph Silk, arXiv:1411.7010, International Journal of Modern Physics D Vol. 23, No. 12, 1442025 (2014).

We propose a new probe to test the nature of gravity at various redshifts through large-scale cosmological observations. We use our void catalog, extracted from the Sloan Digital Sky Survey (SDSS, DR10), to trace the distribution of matter along the lines of sight to SNe Ia that are selected from the Union 2 catalog. We study the relation between SNe Ia luminosities and convergence and also the peculiar velocities of the sources. We show that the effects, on SNe Ia luminosities, of convergence and of peculiar velocities predicted by the theory of general relativity and theories of modified gravities are different and hence provide a new probe of gravity at various redshifts. We show that the present sparse large-scale data does not allow us to determine any statistically- significant deviation from the theory of general relativity but future more comprehensive surveys should provide us with means for such an exploration.

 

14) Expected dipole asymmetry in CMB polarization

M. H. Namjoo, A. A. Abolhasani, H. Assadullahi, S. Baghram, H. Firouzjahi, D. Wands, arXiv:1411.5312, JCAP 05 (2015) 015.

We explore the hemispherical asymmetry predicted in cosmic microwave background polarization when there is an asymmetry in temperature anisotropies due to primordial perturbations. We consider the cases of asymmetries due to adiabatic and isocurvature modes, and tensor perturbations. We show that the asymmetry in the TE, EE and/or BB correlations can be substantially larger than those in the TT power spectrum in certain cases. The relative asymmetry in the different cross-correlations, as well as the angular scale dependence, can in principle distinguish between different origins for the asymmetry.

13)  Fingerprints of Anomalous Primordial Universe on the Abundance of Large Scale Structures

Shant Baghram, Ali Akbar Abolhasani, Hassan Firouzjahi, Mohammad Hossein Namjoo,   arXiv:1406.7277, JCAP 12 (2014) 036.

We study the predictions of anomalous inflationary models on the abundance of structures in large scale structure observations. The anomalous features encoded in primordial curvature perturbation power spectrum are (a): localized feature in momentum space, (b): hemispherical asymmetry and (c): statistical anisotropies. We present a model-independent expression relating the number density of structures to the changes in the matter density variance. Models with localized feature can alleviate the tension between observations and numerical simulations of cold dark matter structures on galactic scales as a possible solution to the missing satellite problem. In models with hemispherical asymmetry we show that the abundance of structures becomes asymmetric depending on the direction of observation to sky. In addition, we study the effects of scale-dependent dipole amplitude on the abundance of structures and, using the quasars data, we find the upper bound nA<0.6 for the spectral index of the dipole asymmetry. In all cases there is a critical mass scale Mc in which for M<Mc(M>Mc) the enhancement in variance induced from anomalous feature decreases (increases) the abundance of dark matter structures in Universe.

12) CMB Hemispherical Asymmetry: Long Mode Modulation and non-Gaussianity

Mohammad Hossein Namjoo, Ali Akbar Abolhasani, Shant Baghram, Hassan Firouzjahi   arXiv:1405.7317 , JCAP 1408 (2014) 002

The observed hemispherical asymmetry in CMB map can be explained by modulation from a long wavelength super horizon mode which non-linearly couples to the CMB modes. We address the criticism in [1] about the role of non-Gaussianities in squeezed and equilateral configurations in generating hemispherical asymmetry from the long mode modulation. We stress that the modulation is sensitive to the non-Gaussianity in the squeezed limit. In addition, we demonstrate the validity of our approach in providing a consistency condition relating the amplitude of dipole asymmetry to f_{NL} in the squeezed limit.

11)Transient Weak-Lensing by Cosmological Dark Matter Microhaloes

Sohrab Rahvar, Shant Baghram, Niayesh Afshordi,   arXiv:1310.5412 , Physical Review D 89, 063001 (2014)

We study the time variation of the apparent flux of cosmological point sources due to the transient weak lensing by dark matter microhaloes. Assuming a transverse motion of microhaloes with respect to our line of sight, we derive the correspondence between the temporal power spectrum of the weak lensing magnification, and the spatial power spectrum of density on small scales. Considering different approximations for the small scale structure of dark matter, we predict the apparent magnitude of cosmological point sources to vary by as much as 10−4−10−3, due to this effect, within a period of a few months. This red photometric noise has an almost perfect gaussian statistics, to one part in  We also comparthe transient weak lensing power spectrum with the background effects such as the stellar microlensing on cosmological scales. A quasar lensed by a galaxy or cluster like SDSSJ1004+4112 strong lensing system, with multiple images, is a suitable system for this study as: (i) using the time-delay method between different images, we can remove the intrinsic variations of the quasar, and (ii) strong lensing enhances signals from the transient weak lensing. We also require the images to form at large angular separations from the center of the lensing structure, in order to minimize contamination by the stellar microlensing. With long-term monitoring of quasar strong lensing systems with a 10-meter class telescope, we can examine the existence of dark microhaloes as the building blocks of dark matter structures. Failure to detect this signal may either be caused by a breakdown of cold dark matter (CDM) hierarchy on small scales, or rather interpreted as evidence against CDM paradigm, e.g. in favor of modified gravity models.

 

 10)Simultaneous effect of Modified Gravity and Primordial Non-Gaussianit

Nareg Mirzatuny, Shahram Khosravi, Shant Baghram, Hossein Moshafi,  arXiv:1308.2874 , Journal of Cosmology and Astroparticle Physics 01(2014) 019

In this work we study the simultaneous effect of primordial non-Gaussianity and the modification of the gravity in $f(R)$ framework on large scale structure observations. We show that non-Gaussianity and modified gravity introduce a scale dependent bias and growth rate functions. The deviation from $\Lambda$CDM in the case of primordial non-Gaussian models is in large scales, while the growth rate deviates from $\Lambda$CDM in small scales for modified gravity theories. We show that the redshift space distortion can be used to distinguish positive and negative $f_{NL}$ in standard background, while in $f(R)$ theories there are not easily distinguishable. The galaxy power spectrum is generally enhanced in presence of non-Gaussianity and modified gravity. We also obtain the scale dependence of this enhancement. Finally we define galaxy growth rate and galaxy growth rate bias as new observational parameters to constrain cosmologyy in Large Scale Structure Observations

 

9)Asymmetric Sky from the Long Mode Modulations

Ali Akbar Abolhasani, Shant Baghram, Hassan Firouzjahi, Mohammad Hossein Namjoo, arXiv:1306.6932, Physical Review D 89, 063511 (2014)

The observed dipole asymmetry in Cosmic Microwave Background radiation may have originated from the modulations of super-horizon long wavelength modes. In this work we unveil different aspects of asymmetries generated from the long wavelength mode modulations. We show that the same mechanism which leads to the observed CMB power spectrum dipole asymmetry from the long mode modulations also yields dipole asymmetry in (a): tensor perturbations power spectrum, (b): the halo bias parameter and (c): late time acceleration expansion. These are different phenomena relevant to different cosmological histories but all share the same underlying mechanism in generating asymmetries in the sky. We obtain the set of consistency conditions relating the amplitude of dipole asymmetries generated on tensor perturbations, halo bias parameter and acceleration expansion to the amplitude of dipole asymmetry generated on CMB power spectrum.

8)Hemispherical Asymmetry and Local non-Gaussianity: a Consistency Condition
Mohammad Hossein Namjoo, Shant Baghram, Hassan Firouzjahi, arXiv:1305.0813, Physical Review D 88, 083527 (2013)

In this paper we provide a consistency relation between the amplitude of the hemispherical bipolar asymmetry, $A$, and the amplitude of the primordial non-Gaussianity in the squeezed limit, $f_{NL}$, as $|A| \lesssim 10^{-1}f_{NL}$. We demonstrate that this consistency condition is at work for any model of inflation in which the curvature perturbations is sourced by a single light field with the Bunch-Davies initial condition, irrespective of the number of inflation fields which contribute to the background inflationary expansion. As a non-trivial example, we show that observable hemispherical asymmetry can be generated in single field non-attractor inflationary models. We also study hemispherical asymmetry generated in the models of multiple fields inflation. We show that $A$ is controlled by the weighted sum of non-Gaussianity contribution from each field. In particular, we show that observable hemispherical asymmetry can be generated in models where inhomogeneities are generated from a light scalar field modulating the surface of end of inflation.

 7) Large Scale Anisotropic Bias from Primordial non-Gaussianity
Shant Baghram, Mohammad Hossein Namjoo, Hassan Firouzjahi, submitted to JCAP, arXiv:1303.4368 (Journal of Cosmology and Astroparticle Physics 08(2013) 048 )

In this work we study the large scale structure bias in models of anisotropic inflation. We use the Peak Background Splitting method in Excursion Set Theory to find the scale-dependent bias. We show that the amplitude of the bias is modified by a direction-dependent factor. In the specific anisotropic inflation model which we study, the scale-dependent bias vanishes at leading order when the long wavelength mode in squeezed limit is aligned with the anisotropic direction in the sky. We also extend the scale-dependent bias formulation to the general situations with primordial anisotropy. We find some selection rules indicating that some specific parts of a generic anisotropic bispectrum is picked up by the bias parameter. We argue that the anisotropic bias is mainly sourced by the angle between the anisotropic direction and the long wavelength mode in the squeezed limit.

 

6)"Prospects for detecting Dark Matter Halo substructure with Pulsar Timing."
Shant Baghram, Niayesh Afshordi, Kathryn Zurik.,
Physical Review D. 84 043511, (2011),

One of the open questions of modern cosmology is the nature and properties of the Dark Matter halo and its substructures. In this work we study the gravitational effect of dark matter substructures on pulsar timing observations. Since millisecond pulsars are stable and accurate emitters, they have been proposed as plausible astrophysical tools to probe the gravitational effects of dark matter structures. We study this effect on pulsar timing through Shapiro time delay (or Integrated Sachs-Wolfe (ISW) effect) and Doppler effects statistically, showing that the latter dominates the signal. For this task, we relate the power spectrum of pulsar frequency change to the matter power spectrum on small scales, which we compute using the stable clustering hypothesis. We compare this power spectrum with the reach of current and future observations of pulsar timing designed for gravitational wave (GW) detection. Our results show that while current observations are unable to detect these signals, the sensitivity of the upcoming Square Kilometer Array (SKA) is only a factor of few weaker than our optimistic predictions.

5)"Structure formation in f(R) gravity: A distinguishing probe between the dark energy and modified gravity. "
Shant Baghram and Sohrab Rahvar , Journal of Cosmology and Astroparticle Physics (JCAP) 12, 008 (2010)

  In this work, we study the large scale structure formation in the modified gravity in the framework of Palatini formalism and compare the results with the equivalent smooth dark energy models as a tool to distinguish between these models. Through the inverse method, we reconstruct the dynamics of universe, modified gravity action and the structure formation indicators like the screened mass function and gravitational slip parameter. Consequently, we extract the matter density power spectrum for these two models in the linear regime and show that the modified gravity and dark energy models predictions are slightly different from each other at large scales. It is also shown that the growth index in the modified gravity unlike to the dark energy models is a scale dependent parameter. We also compare the results with those from the modified gravity in the metric formalism. The modification on the structure formation can also change the CMB spectrum at large scales however due to the cosmic variance it is hard to detect this signature. We show that a large number of SNIa data in the order of 2000 will enable us to reconstruct the modified gravity action with a suitable confidence level and test the cosmic acceleration models by the structure formation.

4)"Inverse problem: Reconstruction of modified gravity action
in Palatini formalism by Supernova Type Ia data" .
Shant Baghram and Sohrab Rahvar, Physical Review D 80, 124049 (2009).

We introduce in $f(R)$ gravity--Palatini formalism the method of inverse problem to extract the action from the expansion history of the universe. First, we use an ansatz for the scale factor and apply the inverse method to derive an appropriate action for the gravity. In the second step we use the Supernova Type Ia data set from the Union sample and obtain a smoothed function for the Hubble parameter up to the redshift~1.7. We apply the smoothed Hubble parameter in the inverse approach and reconstruct the corresponding action in $f(R)$ gravity. In the next step we investigate the viability of reconstruction method, doing a Monte-Carlo simulation we generate synthetic SNIa data with the quality of union sample and show that roughly more than 1500 SNIa data is essential to reconstruct correct action. Finally with the enough SNIa data, we propose two diagnosis in order to distinguish between the $\Lambda$CDM model and an alternative theory for the acceleration of the universe.

3)"Observational tests of a two parameter power-law class modified gravity in Palatini formalism."
Shant Baghram , M.Sadegh Movahed,Sohrab Rahvar, Physical Review D80,064003(2009).

{\bf{CONTEXT}}: In this work we propose a modified gravity action $f(R)=(R^n-R^n_{0})^{1/n}$ with two free parameters of $n$ and $R_{0}$ and derive the dynamics of a universe for this action in the Palatini formalism. {\bf {AIM}}: We do a cosmological comparison of this model with observed data to find the best parameters of a model in a flat universe. {\bf{METHOD}}: To constrain the free parameters of model we use SNIa type Ia data in two sets of gold and union samples, CMB-shift parameter, baryon acoustic oscillation, gas mass fraction in cluster of galaxies, and large-scale structure data. {\bf {RESULT}}: The best fit from the observational data results in the parameters of model in the range of $n=0.98^{+0.08}_{-0.08}$ and $\Omega_M = 0.25_{+0.1}^{-0.1}$ with one sigma level of confidence where a standard $\Lambda$CDM universe resides in this range of solution.

2)"Consistency of f(R) = √R2- R20 Gravity with the Cosmological Observations in Palatini Formalism "
M.Sadegh Movahed,Shant Baghram,Sohrab Rahvar, Physical Review D76,044008(2007).

In this work we study the dynamics of universe in $f(R)=\sqrt{R^2-R_{0}^2}$ modified gravity with Palatini formalism. We use data from recent observations as Supernova Type Ia (SNIa) Gold sample and Supernova Legacy Survey (SNLS) data, size of baryonic acoustic peak from Sloan Digital Sky Survey (SDSS), the position of the acoustic peak from the CMB observations and large scale structure formation (LSS) from the 2dFGRS survey to put constraint on the parameters of the model. To check the consistency of this action, we compare the age of old cosmological objects with the age of universe. In the combined analysis with the all the observations, we find the parameters of model as $R_0=6.192_{-0.177}^{+0.167}\times H_0^2$ and $\Omega_m=0.278_{-0.278}^{+0.273}$.

1)"Modified Gravity with f(R) = √R2- R20"
Shant Baghram,Marzieh Farhang and Sohrab Rahvar, Physical Review D 75,044024(2007)

Here in this work we propose a modified gravity with the action of $f(R) = \sqrt{R^2 - R_0^2}$ instead of Einstein-Hilbert action to describe the late time acceleration of the universe. We obtain the equation of the modified gravity both in the metric and Palatini formalisms. An asymptotic solution of gravity equations corresponding to a constant Ricci scalar causes a late time acceleration of the universe. We do a conformal transformation in the action of the modified gravity and obtain the equivalent minimally coupled scalar-tensor gravity. The equivalent Brans-Dicke gravity of this model is also studied. To examine this model with the observation, the perihelion Precession of the Mercury is compared with our prediction and we put an upper constraint of $R_0<H_0^2$. This range for $R_0$ is also in agreement with the cosmological acceleration at the present time. Finally we show that this action has instability for the small perturbations of the metric in vacuum solution in which adding a quadratic term of Ricci scalar can stabilize it.