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Register a new userCosmology from an exponential dependence on the trace of the energy-momentum tensor -- Numerical approach and cosmological tests
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Added by
Joao Rafael Lucio Dos Santos
Publication date
2019
fields
Physics
and research's language is
English
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In this paper, we present the cosmological scenario obtained from $f(R,T)$ gravity by using an exponential dependence on the trace of the energy-momentum tensor. With a numerical approach applied to the equations of motion, we show several precise fits and the respective cosmological consequences. As a matter of completeness, we also analyzed cosmological scenarios where this new version of $f(R,T)$ is coupled with a real scalar field. In order to find analytical cosmological parameters, we used a slow-roll approximation for the evolution of the scalar field. This approximation allowed us to derived the Hubble and the deceleration parameters whose time evolutions describe the actual phase of accelerated expansion, and corroborate with our numerical investigations. Therefore, the analytical parameters unveil the viability of this proposal for $f(R,T)$ in the presence of an inflaton field.
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We study the effective energy-momentum tensor (EMT) for cosmological perturbations and formulate the gravitational back-reaction problem in a gauge invariant manner. We analyze the explicit expressions for the EMT in the cases of scalar metric fluctuations and of gravitational waves and derive the resulting equations of state. The formalism is applied to investigate the back-reaction effects in chaotic inflation. We find that for long wavelength scalar and tensor perturbations, the effective energy density is negative and thus counteracts any pre-existing cosmological constant. For scalar perturbations during an epoch of inflation, the equation of state is de Sitter-like.
The $f(R,T)$ gravity field equations depend generically on both the Ricci scalar $R$ and trace of the energy-momentum tensor $T$. Within the assumption of perfect fluids, the theory carries an arbitrariness regarding the choice of the matter lagrangian density $mathcal{L}$, not uniquely defined. Such an arbitrariness can be evaded by working with the trace of the theory field equations. From such an equation, one can obtain a form for $mathcal{L}$, which does not carry the arbitrariness. The obtained form for $mathcal{L}$ shows that the $f(R,T)$ gravity is unimodular. A new version of the theory is, therefore, presented and forthcoming applications are expected.
Wormholes are tunnels connecting two different points in space-time. In Einsteins General Relativity theory, wormholes are expected to be filled by exotic matter, i.e., matter that does not satisfy the energy conditions and may have negative density. We propose, in this paper, the achievement of wormhole solutions with no need for exotic matter. In order to achieve so, we consider quadratic terms in the trace of the energy-momentum tensor as corrections to the effective energy-momentum tensor of the underlined theory of gravity. We show that by following this formalism, it is possible, indeed, to obtain non-exotic matter wormhole solutions.
In some inflation scenarios such as $R^{2}$ inflation, a gravitational scalar degrees of freedom called scalaron is identified as inflaton. Scalaron linearly couples to matter via the trace of energy-momentum tensor. We study scenarios with a sequestered matter sector, where the trace of energy-momentum tensor predominantly determines the scalaron coupling to matter. In a sequestered setup, heavy degrees of freedom are expected to decouple from low-energy dynamics. On the other hand, it is non-trivial to see the decoupling since scalaron couples to a mass term of heavy degrees of freedom. Actually, when heavy degrees of freedom carry some gauge charge, the amplitude of scalaron decay to two gauge bosons does not vanish in the heavy mass limit. Here the quantum contribution to the trace of energy-momentum tensor plays an essential role. This quantum contribution is known as trace anomaly or Weyl anomaly. The trace anomaly contribution from heavy degrees of freedom cancels with the contribution from the ${it classical}$ scalaron coupling to a mass term of heavy degrees of freedom. We see how trace anomaly appears both in the Fujikawa method and in dimensional renormalization. In dimensional renormalization, one can evaluate the scalaron decay amplitude in principle at all orders, while it is unclear how to process it beyond the one-loop level in the Fujikawa method. We consider scalaron decay to two gauge bosons via the trace of energy-momentum tensor in quantum electrodynamics with scalars and fermions. We evaluate the decay amplitude at the leading order to demonstrate the decoupling of heavy degrees of freedom.
In this study we consider an exponential decaying form for dark energy as EoS parameter in order to discuss the dynamics of the universe. Firstly, assuming that universe is filled with an ideal fluid which consists of exponential decaying dark energy we obtain time dependent behavior of several physical quantities such as energy density, pressure and others for dark energy, dark energy-matter coupling and non-coupling cases. Secondly, using scalar field instead of an ideal fluid we obtain these physical quantities in terms of scalar potential and kinetic term for the same cases in scalar-tensor formalism. Finally we show that ideal fluid and scalar-tensor description of dark energy give mathematically equivalent results for this EoS parameter.
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