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Register a new userCosmological implications of scale-independent energy-momentum squared gravity: Pseudo nonminimal interactions in dark matter and relativistic relics
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In this paper, we introduce a scale-independent energy-momentum squared gravity (EMSG) that allows different gravitational couplings for different types of sources, which may lead to scenarios with many interesting applications/implications in cosmology. In the present study, to begin with, we study a modification of the $Lambda$ cold dark matter ($Lambda$CDM) model, where photons and baryons couple to the spacetime as in general relativity, while the cold dark matter and relativistic relics (neutrinos and any other relativistic relics) couple to the spacetime in accordance with EMSG. This scenario induces pseudo nonminimal interactions on these components, leading to modification at both the background and perturbative levels. A consequence of this scenario is that the dimensionless free parameter of the theory may induce direct changes on the effective number of the relativistic species, without the need to introduce new extra species. In order to quantify the observational consequences of the cosmological scenario, we use the cosmic microwave background Planck data (temperature, polarization, and lensing power spectrum) and baryonic acoustic oscillations data. We find that the free model parameter is too small to induce statistically significant corrections on the $Lambda$CDM model due to EMSG. We deduce that the model presented here is quite rich with promising cosmological applications/implications that deserve further investigations.
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Deviations from the predictions of general relativity due to energy-momentum squared gravity (EMSG) are expected to become pronounced in the high density cores of neutron stars. We derive the hydrostatic equilibrium equations in EMSG and solve them numerically to obtain the neutron star mass-radius relations for four different realistic equations of state. We use the existing observational measurements of the masses and radii of neutron stars to constrain the free parameter, $alpha ,$ that characterizes the coupling between matter and spacetime in EMSG. We show that $-10^{-38},mathrm{cm^{3}/erg}<alpha <+10^{-37},mathrm{cm^{3}/erg}$. Under this constraint, we discuss what contributions EMSG can provide to the physics of neutron stars, in particular, their relevance to the so called textit{hyperon puzzle} in neutron stars. We also discuss how EMSG alters the dynamics of the early universe from the predictions of the standard cosmological model. We show that EMSG leaves the standard cosmology safely unaltered back to $tsim 10^{-4}$ seconds at which the energy density of the universe is $sim 10^{34},mathrm{erg,cm^{-3}}$.
We consider cosmological models with a dynamical dark energy field, and study the presence of three types of commonly found instabilities, namely ghost (when fields have negative kinetic energy), gradient (negative momentum squared) and tachyon (negative mass squared). In particular, we study the linear scalar perturbations of theories with two interacting scalar fields as a proxy for a dark energy and matter fields, and explicitly show how canonical transformations relate these three types of instabilities with each other. We generically show that low-energy ghosts are equivalent to tachyonic instabilities, and that high-energy ghosts are equivalent to gradient instabilities. Via examples we make evident the fact that whenever one of these fields exhibits an instability then the entire physical system becomes unstable, with an unbounded Hamiltonian. Finally, we discuss the role of interactions between the two fields, and show that whereas most of the time interactions will not determine whether an instability is present or not, they may affect the timescale of the instability. We also find exceptional cases in which the two fields are ghosts and hence the physical system is seemingly unstable, but the presence of interactions actually lead to stable solutions. These results are very important for assessing the viability of dark energy models that may exhibit ghost, gradient or tachyonic modes.
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.
We argue that the $Lambda$CDM tensions of the Hubble-Lemaitre expansion rate $H_0$ and the clustering normalization $sigma_8$ can be eased, at least in principle, by considering an interaction between dark energy and dark matter in such a way to induce a small and positive early effective equation of state and a weaker gravity. For a dark energy scalar field $phi$ interacting with dark matter through an exchange of both energy and momentum, we derive a general form of the Lagrangian allowing for the presence of scaling solutions. In a subclass of such interacting theories, we show the existence of a scaling $phi$-matter-dominated-era ($phi$MDE) which can potentially alleviate the $H_0$ tension by generating an effective high-redshift equation of state. We also study the evolution of perturbations for a model with $phi$MDE followed by cosmic acceleration and find that the effective gravitational coupling relevant to the linear growth of large-scale structures can be smaller than the Newton gravitational constant $G$ at low redshifts. The momentum exchange between dark energy and dark matter plays a crucial role for realizing weak gravity, while the energy transfer is also required for the existence of $phi$MDE.
Several attempts have been made in the past decades to search for the true ground state of the dense matter at sufficiently large densities and low temperatures via compact astrophysical objects. Focusing on strange stars, we derive the hydrostatic equilibrium assuming a maximally symmetric phase of homogeneous superconducting quark matter called the textit{color-flavor-locked} (CFL) phase in the background of energy-momentum squared gravity (EMSG). Theoretical and experimental investigations show that strange quark matter (SQM) in a CFL state can be the true ground state of hadronic matter at least for asymptotic densities, and even if the unequal quark masses. Motivated by these theoretical models, we explore the structure of stellar objects in recently proposed EMSG, which allows a correction term $T_{mu u}T^{mu u}$ in the action functional of the theory. Interestingly, EMSG may be effective to resolve the problems at high energy densities, e.g., relevant to the early universe and dense compact astrophysical objects without invoking some new forms of fluid stress, such as bulk viscosity or scalar fields. Finally, we solve the complicated field equations numerically to obtain the mass-radius relations for strange stars in CFL equation of state.
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