Growth Diagnostics for Dark Energy models and EUCLID forecast

In this work we introduce a new set of parameters $(r_{g}, s_{g})$ involving the linear growth of matter perturbation that can distinguish and constrain different dark energy models very efficiently. Interestingly, for $\Lambda$CDM model these parameters take exact value $(1,1)$ at all red shifts whereas for models different from $\Lambda$CDM, they follow different trajectories in the $(r_{g}, s_{g})$ phase plane. By considering the parametrization for the dark energy equation of state ($w$) and for the linear growth rate ($f_{g}$), we show that different dark energy behaviours with similar evolution of the linear density contrast, can produce distinguishable trajectories in the $(r_{g}, s_{g})$ phase plane. Moreover, one can put stringent constraint on these phase plane using future measurements like EUCLID ruling out some of the dark energy behaviours.Comment: Substantial Revision. EUCLID forecast included. Change in the Title. Overall conclusion remains the sam

GCG Parametrization for Growth Function and Current Constraints

We study the linear growth function $f$ for large scale structures in a cosmological scenario where Generalised Chaplygin Gas (GCG) serves as dark energy candidate. We parametrize the growth index parameter as a function of redshift and do a comparative study between the theoretical growth rate and the proposed parametrization. Moreover, we demonstrate that growth rates for a wide range of dark energy models can be modeled accurately by our proposed parametrization. Finally, we compile a data set consisting of 28 data points within redshift range (0.15,3.8) to constrain the growth rate. It includes direct growth data from various projects/surveys including the latest data from the Wiggle-Z measurements. It also includes data constraining growth indirectly through the rms mass fluctuation $\sigma_8(z)$ inferred from Ly-$\alpha$ measurements at various redshifts. By fitting our proposed parametrization for $f$ to these data, we show that growth history of large scale structures of the universe although allows a transient acceleration, one cannot distinguish it at present with an eternally accelerating universe.Comment: 19 pages, Latex Style, 5 EPS figures, 3 Tables, Revised and improved versio

Black Holes and Generalized Scalar Field

We study the possibility of occurrence of scalar hair with a non-canonical kinetic term for a static, spherically symmetric asymptotically flat black hole spacetime. We first obtain a general equation for this purpose and then consider various examples for the kinetic term $F(X)$ with $X=-{1\over{2}}\partial^{\mu}\phi\partial_{\mu}\phi$. Our study shows that for a tachyon field with a positive potential, which naturally arises in open string theory, asymptotically flat a static black hole solution does not exist.Comment: 8 pages, LaTeX with elsart styl

Astrophysical Signatures of Black holes in Generalized Proca Theories

Explaining the late time acceleration is one of the most challenging tasks for theoretical physicists today. Infra-red modification of Einstein's general theory of relativity (GR) is a possible route to model late time acceleration. In this regard, vector-tensor theory as a part of gravitational interactions on large cosmological scales, has been proposed recently. This involves generalization of massive Proca lagrangian in curved space time. Black hole solutions in such theories have also been constructed. In this paper, we study different astrophysical signatures of such black holes. We first study the strong lensing and time delay effect of such static spherically symmetric black hole solutions, in particular for the case of gravitational lensing of the star S2 by Sagittarius A* at the centre of Milky Way. We also construct the rotating black hole solution from this static spherically symmetric solution in Proca theories using the Newman-Janis algorithm and subsequently study lensing, time delay and black hole shadow effect in this rotating black hole space time. We discuss the possibility of detecting Proca hair in future observations.Comment: 19 pages, 7 figures, Accepted for publication in Physical Review

Clustering GCG: a viable option for unified dark matter-dark energy?

We study the clustering Generalized Chaplygin Gas (GCG) as a possible candidate for dark matter-dark energy unification. The vanishing speed of sound ($c_{s}^2 = 0$) for the GCG fluid can be obtained by incorporating higher derivative operator in the original K-essence Lagrangian. The evolution of the density fluctuations in the GCG+Baryon fluid is studied in the linear regime. The observational constraints on the model are obtained using latest data from SNIa, $H(z)$, BAO and also for the $f\sigma_{8}$ measurements. The matter power spectra for the allowed parameter values are well behaved without any unphysical features.Comment: 11 pages, Latex style, 6 eps figure

A new recipe for Λ\LambdaCDM

It is well known that a canonical scalar field is able to describe either dark matter or dark energy but not both. We demonstrate that a non-canonical scalar field can describe both dark matter and dark energy within a unified setting. We consider the simplest extension of the canonical Lagrangian ${\cal L} \propto X^\alpha - V(\phi)$ where $\alpha \geq 1$ and $V$ is a sufficiently flat potential. In this case the kinetic term in the Lagrangian behaves just like a perfect fluid, whereas the potential term mimicks the cosmological constant. For very large values, $\alpha \gg 1$, the equation of state of the kinetic term drops to zero and the expansion rate of the universe mimicks $\Lambda$CDM. The velocity of sound in this model, and the associated gravitational clustering, is sensitive to the value of $\alpha$. For very large values of $\alpha$ the clustering properties of our model resemble those of cold dark matter (CDM). But for smaller values of $\alpha$, gravitational clustering on small scales is suppressed, and our model has properties resembling those of warm dark matter (WDM). Therefore our non-canonical model has an interesting new property: while the background universe expands like $\Lambda$CDM, its clustering properties can resemble those of either cold or warm dark matter.Comment: 16 pages, 4 figures. Additional new results, main conclusions strengthene

The Price of Shifting the Hubble Constant

An anisotropic measurement of the baryon acoustic oscillation (BAO) feature fixes the product of the Hubble constant and the acoustic scale $H_0 r_d$. Therefore, regardless of the dark energy dynamics, to accommodate a higher value of $H_0$ one needs a lower $r_d$ and so necessarily a modification of early time cosmology. One must either reduce the age of the Universe at the drag epoch or else the speed of sound in the primordial plasma. The first can be achieved, for example, with dark radiation or very early dark energy, automatically preserving the angular size of the acoustic scale in the Cosmic Microwave Background (CMB) with no modifications to post-recombination dark energy. However it is known that the simplest such modifications fall afoul of CMB constraints at higher multipoles. As an example, we combine anisotropic BAO with geometric measurements from strong lensing time delays from H0LiCOW and megamasers from the Megamaser Cosmology Project to measure $r_d$, with and without the local distance ladder measurement of $H_0$. We find that the best fit value of $r_d$ is indeed quite insensitive to the dark energy model, and is also hardly affected by the inclusion of the local distance ladder data.Comment: 33 pages, 25 PDF figure

Imprint of thawing scalar fields on large scale galaxy overdensity

We investigate the observed galaxy power spectrum for the thawing class of scalar field models taking into account various general relativistic corrections that occur on very large scales. We consider the full general relativistic perturbation equations for the matter as well as the dark energy fluid. We form a single autonomous system of equations containing both the background and perturbed equations of motion which we subsequently solve for different scalar field potentials. First we study the percentage deviation from $\Lambda$CDM model for different cosmological parameters as well as in the observed galaxy power spectra on different scales in scalar field models for various choices of scalar field potentials. Interestingly the difference in background expansion results enhancement of power from $\Lambda$CDM on small scales whereas the inclusion of GR corrections results the suppression of power from $\Lambda$CDM on large scales. This can be useful to distinguish scalar field models from $\Lambda$CDM with future optical/radio surveys. We also compare the observed galaxy power spectra for tracking and thawing types of scalar field using some particular choices for the scalar field potentials. We show that thawing and tracking models can have large differences in observed galaxy power spectra on large scales and for smaller redshifts due to different GR effects. But on smaller scales and for larger redshifts, the difference is small and is mainly due to difference in background expansion.Comment: Revised version with new results, comments welcom

Non-Minimal Quintessence With Nearly Flat Potential

We consider Brans-Dicke type nonminimally coupled scalar field as a candidate for dark energy. In the conformally transformed Einstein's frame, our model is similar to {\it coupled quintessence} model. In such models, we consider potentials for the scalar field which satisfy the slow-roll conditions: $[(1/V)(dV/d\phi)]^2 << 1$ and $(1/V)(d^2V/d\phi^2) << 1$. For such potentials, we show that the equation of state for the scalar field can be described by a universal behaviour, provided the scalar field rolls only in the flat part of the potentials where the slow-roll conditions are satisfied. Our work generalizes the previous work by Scherrer and Sen \cite{scherrer} for minimally coupled scalar field case. We have also studied the observational constraints on the model parameters considering the Supernova and BAO observational data

Is it time to go beyond Λ\LambdaCDM universe?

Concordance $\Lambda$CDM universe is the simplest model that is consistent with a large variety of cosmological observations till date. But few recent observations indicate inconsistencies in $\Lambda$CDM model. In this paper, we consider the combination of recent SnIa+Bao+Cmb+Growth+$H(z)$+$H_{0}$ measurements to revisit the constraints on the dark energy evolution using the widely studied CPL parametrisation for the dark energy equation of state. Although the reconstructed behaviour for the dark energy equation of state confirms the inconsistency of $\Lambda$CDM at $95\%$ confidence level, the reconstructed $Om$ diagnostic which is a {\it null test} for $\Lambda$CDM, still allows the concordance $\Lambda$CDM behaviour with a lower range of $\Omega_{m0}$ than that obtained by Planck-2015. {\it This confirms that $\Lambda$CDM is still the best choice for the dark energy model}. We also measure the parameter $S = \sigma_{8}\sqrt{\Omega_{m0}/0.3} = 0.728 \pm 0.023$ which is consistent with its recent measurement by KiDS survey. The confidence contour in the $\Omega_{m0}-\sigma_{8}$ parameter plane is also fully consistent with KiDS survey measurement.Comment: 13 pages, LateX style, 1 table, 6 eps figures. New References and figures added. Conclusions remain the sam