Generalising the matter coupling in massive gravity: a search for new interactions

Massive gravity theory introduced by de Rham, Gabadadze, Tolley (dRGT) is restricted by several uniqueness theorems that protect the form of the potential and kinetic terms, as well as the matter coupling. These restrictions arise from the requirement that the degrees of freedom match the expectation from Poincar\'e representations of a spin--2 field. Any modification beyond the dRGT form is known to invalidate a constraint that the theory enjoys and revive a dangerous sixth mode. One loophole is to exploit the effective nature of the theory by pushing the sixth mode beyond the strong coupling scale without completely removing it. In this paper, we search for modifications to dRGT action by coupling the matter sector to an arbitrary metric constructed out of the already existing degrees of freedom in the dRGT action. We formulate the conditions that such an extension should satisfy in order to prevent the sixth mode from contaminating the effective theory. Our approach provides a new perspective for the "composite coupling" which emerges as the unique extension up to four-point interactions.Comment: 19 pages; v2: new references added, accepted for publication in PR

Quasi Non-linear Evolution of Stochastic Bias

It is generally believed that the spatial distribution of galaxies does not trace that of the total mass. The understanding of the bias effect is therefore necessary to determine the cosmological parameters and the primordial density fluctuation spectrum from the galaxy survey. The deterministic description of bias may not be appropriate because of the various stochasticity of galaxy formation process. In nature, the biasing is epoch dependent and recent deep survey of the galaxy shows the large biasing at high redshift. Hence, we investigate quasi non-linear evolution of the stochastic bias by using the tree level perturbation method. Especially, the influence of the initial cross correlation on the evolution of the skewness and the bi-spectrum is examined in detail. We find that the non-linear bias can be generated dynamically. The small value of the initial cross correlation can bend the \dg-\dm relation effectively and easily lead to the negative curvature ($b_2<0$). We also propose a method to predict the bias, cross correlation and skewness at high redshift. As an illustration, the possibility of the large biasing at high redshift is discussed. Provided the present bias parameter as $b=1.5$ and $\Omega=1.0$, we predict the large scale bias as $b=4.63$ at $z=3$ by fitting the bi-spectrum to the Lick catalog data. Our results will be important for the future deep sky survey.Comment: 20 pages, 5 Encapsulated Postscript figures, aastex, final version to appear in Ap

Scalar perturbations in braneworld cosmology

We study the behaviour of scalar perturbations in the radiation-dominated era of Randall-Sundrum braneworld cosmology by numerically solving the coupled bulk and brane master wave equations. We find that density perturbations with wavelengths less than a critical value (set by the bulk curvature length) are amplified during horizon re-entry. This means that the radiation era matter power spectrum will be at least an order of magnitude larger than the predictions of general relativity (GR) on small scales. Conversely, we explicitly confirm from simulations that the spectrum is identical to GR on large scales. Although this magnification is not relevant for the cosmic microwave background or measurements of large scale structure, it will have some bearing on the formation of primordial black holes in Randall-Sundrum models.Comment: 17 pages, 7 figure

Assessing non-linear models for galaxy clustering III: Theoretical accuracy for Stage IV surveys

We provide in depth MCMC comparisons of two different models for the halo redshift space power spectrum, namely a variant of the commonly applied Taruya-Nishimichi-Saito (TNS) model and an effective field theory of large scale structure (EFTofLSS) inspired model. Using many simulation realisations and Stage IV survey-like specifications for the covariance matrix, we check each model's range of validity by testing for bias in the recovery of the fiducial growth rate of structure formation. The robustness of the determined range of validity is then tested by performing additional MCMC analyses using higher order multipoles, a larger survey volume and a more highly biased tracer catalogue. We find that under all tests, the TNS model's range of validity remains robust and is found to be much higher than previous estimates. The EFTofLSS model fails to capture the spectra for highly biased tracers as well as becoming biased at higher wavenumbers when considering a very large survey volume. Further, we find that the marginalised constraints on $f$ for all analyses are stronger when using the TNS model.Comment: 25 pages, 19 figures. Accepted version for publication in JCA

Quantum-mechanical generation of gravitational waves in braneworld

We study the quantum-mechanical generation of gravitational waves during inflation on a brane embedded in a five-dimensional anti-de Sitter bulk. To make the problem well-posed, we consider the setup in which both initial and final phases are given by a de Sitter brane with different values of the Hubble expansion rate. Assuming that the quantum state is in a de Sitter invariant vacuum in the initial de Sitter phase, we numerically evaluate the amplitude of quantum fluctuations of the growing solution of the zero mode in the final de Sitter phase. We find that the vacuum fluctuations of the initial Kaluza-Klein gravitons as well as of the zero mode gravitons contribute to the final amplitude of the zero mode on small scales, and the power spectrum is quite well approximated by what we call the rescaled spectrum, which is obtained by rescaling the standard four-dimensional calculation following a simple mapping rule. Our results confirm the speculation raised in Ref. \cite{Kobayashi:2003cn} before.Comment: 11 pages, 11 figure

Inflaton perturbations in brane-world cosmology with induced gravity

We study cosmological perturbations in the brane models with an induced Einstein-Hilbert term on a brane. We consider an inflaton confined to a de Sitter brane in a five-dimensional Minkowski spacetime. Inflaton fluctuations excite Kaluza-Klein modes of bulk metric perturbations with mass $m^2 = -2(2\ell-1) (\ell +1) H^2$ and $m^2 = -2\ell(2\ell+3) H^2$ where $\ell$ is an integer. There are two branches ($\pm$ branches) of solutions for the background spacetime. In the $+$ branch, which includes the self-accelerating universe, a resonance appears for a mode with $m^2 = 2 H^2$ due to a spin-0 perturbation with $m^2 = 2H^2$. The self-accelerating universe has a distinct feature because there is also a helicity-0 mode of spin-2 perturbations with $m^2 = 2H^2$. In the $-$ branch, which can be thought as the Randall-Sundrum type brane-world with the high energy quantum corrections, there is no resonance. At high energies, we analytically confirm that four-dimensional Einstein gravity is recovered, which is related to the disappearance of van Dam-Veltman-Zakharov discontinuity in de Sitter spacetime. On sufficiently small scales, we confirm that the lineariaed gravity on the brane is well described by the Brans-Dicke theory with $\omega=3Hr_c$ in $-$ branch and $\omega = -3H r_c$ in $+$ branch, respectively, which confirms the existence of the ghost in $+$ branch. We also study large scale perturbations. In $+$ branch, the resonance induces a non-trivial anisotropic stress on the brane via the projection of Weyl tensor in the bulk, but no instability is shown to exist on the brane.Comment: 20 pages, 4 figure

Stable cosmology in ghost-free quasidilaton theory

We present a novel cosmological solution in the framework of extended quasidilaton theory which underwent scrutiny recently. We only consider terms that do not generate the Boulware-Deser degree of freedom, hence the "ghost-free" quasidilaton theory, and show three new branches of cosmological evolution therein. One of the solutions passes the perturbative stability tests. This new solution exhibits a late time self-acceleration and all graviton polarizations acquire masses that converge to a constant in the asymptotic future. Moreover, all modes propagate at the speed of light. We propose that this solution can be used as a benchmark model for future phenomenological studies.Comment: 12 page

Role of matter in extended quasidilaton massive gravity

The extended quasidilaton theory is one of the simplest Lorentz-invariant massive gravity theories which can accommodate a stable self-accelerating vacuum solution. In this paper we revisit this theory and study the effect of matter fields. For a matter sector that couples minimally to the physical metric, we find hints of a Jeans type instability in the IR. In the analogue k-essence field set-up, this instability manifests itself as an IR ghost for the scalar field perturbation, but this can be interpreted as a classical instability that becomes relevant below some momentum scale in terms of matter density perturbations. We also consider the effect of the background evolution influenced by matter on the stability of the gravity sector perturbations. In particular, we address the previous claims of ghost instability in the IR around the late time attractor. We show that, although the matter-induced modification of the evolution potentially brings tension to the stability conditions, one goes beyond the regime of validity of the effective theory well before the solutions become unstable. We also draw attention to the fact that the IR stability conditions are also enforced by the existence requirements of consistent background solutions.Comment: 17 pages, accepted for publication in PR