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Register a new userGauge transformation of scalar induced tensor perturbation during matter domination
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We study the scalar induced tensor perturbations at second order during matter domination in seven different gauges. Considering the obtained solution from the Newtonian gauge, we use the gauge transformation law of the scalar induced tensor perturbation to derive the solution in six other gauges. After identifying and eliminating the residual gauge modes in the synchronous and comoving orthogonal gauges, we obtain the same analytical results of the kernel function $I_{chi}$ for these two gauges as those obtained from the gauge transformation. For the scalar induced gravitational waves oscillating as $sin x$ and $cos x$, we find that $rho_{text{GW}}propto a^{-4}$, and $Omega_{text{GW}}propto 1/a$ in the matter dominated era, so the oscillating gravitational waves behave as radiation.
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The gauge dependence of the scalar induced gravitational waves (SIGWs) generated at the second order imposes a challenge to the discussion of the secondary gravitational waves generated by scalar perturbations. We provide a general formula that is valid in any gauge for the calculation of SIGWs and the relationship for SIGWs calculated in various gauges under the coordinate transformation. The formula relating SIGWs in the Newtonian gauge to other gauges is used to calculate SIGWs in six different gauges. We find that the Newtonian gauge, the uniform curvature gauge, the synchronous gauge and the uniform expansion gauge yield the same result for the energy density of SIGWs. We also identify and eliminate the pure gauge modes that exist in the synchronous gauge. In the total matter gauge and the comoving orthogonal gauge, the energy density of SIGWs increases as $eta^2$. While in the uniform density gauge, the energy density of SIGWs increases as $eta^6$.
In scalar-vector-tensor (SVT) theories with parity invariance, we perform a gauge-ready formulation of cosmological perturbations on the flat Friedmann-Lema^{i}tre-Robertson-Walker (FLRW) background by taking into account a matter perfect fluid. We derive the second-order action of scalar perturbations and resulting linear perturbation equations of motion without fixing any gauge conditions. Depending on physical problems at hand, most convenient gauges can be chosen to study the development of inhomogeneities in the presence of scalar and vector fields coupled to gravity. This versatile framework, which encompasses Horndeski and generalized Proca theories as special cases, is applicable to a wide variety of cosmological phenomena including nonsingular cosmology, inflation, and dark energy. By deriving conditions for the absence of ghost and Laplacian instabilities in several different gauges, we show that, unlike Horndeski theories, it is possible to evade no-go arguments for the absence of stable nonsingular bouncing/genesis solutions in both generalized Proca and SVT theories. We also apply our framework to the case in which scalar and vector fields are responsible for dark energy and find that the separation of observables relevant to the evolution of matter perturbations into tensor, vector, and scalar sectors is transparent in the unitary gauge. Unlike the flat gauge chosen in the literature, this result is convenient to confront SVT theories with observations associated with the cosmic growth history.
Matter bounces refer to scenarios wherein the universe contracts at early times as in a matter dominated epoch until the scale factor reaches a minimum, after which it starts expanding. While such scenarios are known to lead to scale invariant spectra of primordial perturbations after the bounce, the challenge has been to construct completely symmetric bounces that lead to a tensor-to-scalar ratio which is small enough to be consistent with the recent cosmological data. In this work, we construct a model involving two scalar fields (a canonical field and a non-canonical ghost field) to drive the symmetric matter bounce and study the evolution of the scalar perturbations in the model. If we consider the scale associated with the bounce to be of the order of the Planck scale, the model is completely described in terms of only one parameter, viz the value of the scale factor at the bounce. We evolve the scalar perturbations numerically across the bounce and evaluate the scalar power spectra after the bounce. We show that, while the scalar and tensor perturbation spectra are scale invariant over scales of cosmological interest, the tensor-to-scalar ratio proves to be much smaller than the current upper bound from the observations of the cosmic microwave background anisotropies by the Planck mission. We also support our numerical analysis with analytical arguments.
Phenomenological implications of the Mimetic Tensor-Vector-Scalar theory (MiTeVeS) are studied. The theory is an extension of the vector field model of mimetic dark matter, where a scalar field is also incorporated, and it is known to be free from ghost instability. In the absence of interactions between the scalar field and the vector field, the obtained cosmological solution corresponds to the General theory of Relativity (GR) with a minimally-coupled scalar field. However, including an interaction term between the scalar field and the vector field yields interesting dynamics. There is a shift symmetry for the scalar field with a flat potential, and the conserved Noether current, which is associated with the symmetry, behaves as a dark matter component. Consequently, the solution contains a cosmological constant, dark matter and a stiff matter fluid. Breaking the shift symmetry with a non-flat potential gives a natural interaction between dark energy and dark matter.
Recently, it was proposed that a small true vacuum universe can inflate spontaneously, in principle. Furthermore, there should be matter creation in vacuum inflation due to quantum fluctuations, and the matter created will influence the inflation simultaneously. In this paper, scalar and tensor perturbations in this model are analyzed and confronted with recent observations. These perturbations are derived and expressed with Hubble flow-functions. By comparing our calculations with experimental results, we can determine all the parameters in this model. Finally, with the determined parameters, we compute the evolution of the matter density and show that the matter produced in inflation roughly fits the observations at present.
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