A Multi-Parameter Investigation of Gravitational Slip

📝 Abstract

A detailed analysis of gravitational slip, a new post-general relativity cosmological parameter characterizing the degree of departure of the laws of gravitation from general relativity on cosmological scales, is presented. This phenomenological approach assumes that cosmic acceleration is due to new gravitational effects; the amount of spacetime curvature produced per unit mass is changed in such a way that a universe containing only matter and radiation begins to accelerate as if under the influence of a cosmological constant. Changes in the law of gravitation are further manifest in the behavior of the inhomogeneous gravitational field, as reflected in the cosmic microwave background, weak lensing, and evolution of large-scale structure. The new parameter, $\varpi_0 $, is naively expected to be of order unity. However, a multiparameter analysis, allowing for variation of all the standard cosmological parameters, finds that $\varpi_0 = 0.09^{+0.74}_{-0.59} (2\sigma)$ where $\varpi_0=0$ corresponds to a $\Lambda $CDM universe under general relativity. Future probes of the cosmic microwave background (Planck) and large-scale structure (Euclid) may improve the limits by a factor of four.

💡 Analysis

A detailed analysis of gravitational slip, a new post-general relativity cosmological parameter characterizing the degree of departure of the laws of gravitation from general relativity on cosmological scales, is presented. This phenomenological approach assumes that cosmic acceleration is due to new gravitational effects; the amount of spacetime curvature produced per unit mass is changed in such a way that a universe containing only matter and radiation begins to accelerate as if under the influence of a cosmological constant. Changes in the law of gravitation are further manifest in the behavior of the inhomogeneous gravitational field, as reflected in the cosmic microwave background, weak lensing, and evolution of large-scale structure. The new parameter, $\varpi_0 $, is naively expected to be of order unity. However, a multiparameter analysis, allowing for variation of all the standard cosmological parameters, finds that $\varpi_0 = 0.09^{+0.74}_{-0.59} (2\sigma)$ where $\varpi_0=0$ corresponds to a $\Lambda $CDM universe under general relativity. Future probes of the cosmic microwave background (Planck) and large-scale structure (Euclid) may improve the limits by a factor of four.

📄 Content

arXiv:0901.0919v2 [astro-ph.CO] 3 Aug 2009 A Multi-Parameter Investigation of Gravitational Slip Scott F. Daniel∗,1 Robert R. Caldwell,1 Asantha Cooray,2 Paolo Serra,2 and Alessandro Melchiorri3 1Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755 USA 2Department of Physics and Astronomy, University of California, Irvine, CA 92697 USA 3Physics Department and Sezione INFN, University of Rome, “La Sapienza,” P.le Aldo Moro 2, 00185 Rome, Italy (Dated: October 23, 2018) A detailed analysis of gravitational slip, a new post-general relativity cosmological parameter char- acterizing the degree of departure of the laws of gravitation from general relativity on cosmological scales, is presented. This phenomenological approach assumes that cosmic acceleration is due to new gravitational effects; the amount of spacetime curvature produced per unit mass is changed in such a way that a Universe containing only matter and radiation begins to accelerate as if under the influence of a cosmological constant. Changes in the law of gravitation are further manifest in the behavior of the inhomogeneous gravitational field, as reflected in the cosmic microwave background, weak lensing, and evolution of large-scale structure. The new parameter, ̟0, is naively expected to be of order unity. However, a multiparameter analysis, allowing for variation of all the standard cosmological parameters, finds that ̟0 = 0.09+0.74 −0.59 (2σ) where ̟0 = 0 corresponds to a ΛCDM universe under general relativity. Future probes of the cosmic microwave background (Planck) and large-scale structure (Euclid) may improve the limits by a factor of four. I. INTRODUCTION Cosmic acceleration [1, 2] can be caused by new fluids, new theories of gravity, or some admixture of both [3]. This uncertainty places a premium on descriptions of the so-called “dark physics” which remain useful across dif- ferent models and in spite of varying assumptions. In the case of new fluids (dark energy), the literature chooses to speak in terms of the equation of state w and its derivative [4]. In the case of new gravitational physics, the model-independent lingua franca is the relationship between the Newtonian (ψ) and longitudinal (φ) grav- itational potentials. The potentials, implicitly defined through the perturbed Robertson-Walker metric ds2 = a2[−(1 + 2ψ)dτ 2 + (1 −2φ)d⃗x2], (1) are most familiar for their roles in Newton’s equation, ¨⃗x = −⃗∇ψ, and the Poisson equation, ∇2φ = 4πGa2δρ under general relativity (GR). The gravitational potentials are equal in the presence of non-relativistic stress-energy under GR. Alternate the- ories of gravity make no such guarantee. Scalar-tensor [5, 6] and f(R) theories [7, 8, 9], braneworld scenarios such as Dvali-Gabadadze-Porrati gravity [10, 11, 12], and massive gravity [13, 14] all predict a systematic difference or “slip”, so that φ ̸= ψ in the presence of non-relativistic stress-energy. Efforts to develop a parametrized-post- Friedmannian (PPF) framework to phenomenologically describe this behavior are just as prolific: Refs. [15, 16, 17, 18, 19, 20, 21, 22, 23, 24] all offer parametrizations quantifying the departure from φ = ψ due to new gravi- tational effects. We choose to work with the parametriza- ∗scott.f.daniel@dartmouth.edu tion proposed in Ref. [16]: ψ = [1 + ̟(z)]φ (2) ̟(z) = ̟0(1 + z)−3. (3) We assume the existence of a theory of gravitation that leads to an expansion history that is indistinguishable from that produced by a spatially-flat, ΛCDM scenario with density parameters Ωm and ΩΛ = 1 −Ωm. This assumption is not essential, but it allows our analy- sis to focus solely on PPF effects. Our naive expec- tation is that ̟ ≃ΩΛ/Ωm by today. [Note that we have changed our notation, having previously defined ̟(z) = ̟0(ΩΛ/Ωm)(1 + z)−3.] The departure from GR kicks in only when the cosmic expansion begins to accelerate. Daniel et al. [22] (hereafter DCCM) discuss the compatibility with other parametrizations (especially that of Ref. [23]) and compare the implications of ̟0 ̸= 0 to data from the Wilkinson Microwave Anisotropy Probe (WMAP) [25], the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) [26], and various galaxy surveys [27, 28, 29]. We expand upon their analysis in this work by perform- ing a full likelihood analysis of the cosmological parame- ter space. The previous work by DCCM considered the effects of modified gravity on cosmological perturbations in a one- parameter context: i.e., “how does the the new (modi- fied gravity) parameter affect cosmological data when all other parameters are held fixed (at the WMAP 3 year maximum likelihood values)?” They used a modified version of the Boltzmann code CMBfast [30] to evalu- ate the effect of ̟0 on the cosmic microwave background (CMB) anisotropy, matter power spectrum, weak lensing convergence correlation function, and galaxy-CMB cross- correlation power spectrum. While this analysis was use- ful for testing for the existence of PPF effects, the results

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