Equivalence between fourth-order theories of gravity and general relativity: Possible implications for the cosmological singularity

1987 ◽  
Vol 35 (2) ◽  
pp. 480-482 ◽  
Author(s):  
G. Le Denmat ◽  
H. Sirousse Zia
Keyword(s):  
General Relativity ◽  
Fourth Order ◽  
Cosmological Singularity ◽  
Theories Of Gravity

scholarly journals Breaking the cosmological background degeneracy by two-fluid perturbations in f(R) gravity

2015 ◽  
Vol 24 (07) ◽  
pp. 1550053 ◽  
Author(s):  
Amare Abebe
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Structure Formation ◽  
Background Level ◽  
Cosmological Perturbations ◽  
Gauge Invariant ◽  
First Order ◽  
Cosmological Background ◽  
Theories Of Gravity ◽  
Two Fluid

One of the exact solutions of f(R) theories of gravity in the presence of different forms of matter exactly mimics the ΛCDM solution of general relativity (GR) at the background level. In this work we study the evolution of scalar cosmological perturbations in the covariant and gauge-invariant formalism and show that although the background in such a model is indistinguishable from the standard ΛCDM cosmology, this degeneracy is broken at the level of first-order perturbations. This is done by predicting different rates of structure formation in ΛCDM and the f(R) model both in the complete and quasi-static regimes.

scholarly journals CAN f(R) GRAVITY MIMIC GENERAL RELATIVITY?

2012 ◽  
Vol 10 ◽  
pp. 63-68 ◽  
Author(s):  
JE-AN GU
Keyword(s):  
General Relativity ◽  
Differential Equations ◽  
Early Time ◽  
Einstein Equations ◽  
Modified Theories Of Gravity ◽  
Cosmological Perturbations ◽  
Long Run ◽  
Theories Of Gravity ◽  
The Stability ◽  
Higher Order Differential Equations

We discuss the stability of the general-relativity (GR) limit in modified theories of gravity, particularly the f(R) theory. The problem of approximating the higher-order differential equations in modified gravity with the Einstein equations (2nd-order differential equations) in GR is elaborated. We demonstrate this problem with a heuristic example involving a simple ordinary differential equation. With this example we further present the iteration method that may serve as a better approximation for solving the equation, meanwhile providing a criterion for assessing the validity of the approximation. We then discuss our previous numerical analyses of the early-time evolution of the cosmological perturbations in f(R) gravity, following the similar ideas demonstrated by the heuristic example. The results of the analyses indicated the possible instability of the GR limit that might make the GR approximation inaccurate in describing the evolution of the cosmological perturbations in the long run.

scholarly journals Fourth order deformed general relativity

2014 ◽  
Vol 90 (10) ◽  
Author(s):  
Rhiannon Cuttell ◽  
Mairi Sakellariadou
Keyword(s):  
General Relativity ◽  
Fourth Order

scholarly journals The radiation instability in modified gravity

2021 ◽  
Vol 36 (08n09) ◽  
pp. 2150060
Author(s):  
Spiros Cotsakis ◽  
Dimitrios Trachilis
Keyword(s):  
General Relativity ◽  
General Solution ◽  
Modified Gravity ◽  
Evolution Equations ◽  
Formal Series ◽  
Series Expansions ◽  
General Polynomial ◽  
Theories Of Gravity ◽  
Polynomial Extensions

We study the problem of the instability of inhomogeneous radiation universes in quadratic Lagrangian theories of gravity written as a system of evolution equations with constraints. We construct formal series expansions and show that the resulting solutions have a smaller number of arbitrary functions than that required in a general solution. These results continue to hold for more general polynomial extensions of general relativity.

scholarly journals Quantum interference in external gravitational fields beyond General Relativity

2021 ◽  
Vol 81 (10) ◽  
Author(s):  
Luca Buoninfante ◽  
Gaetano Lambiase ◽  
Luciano Petruzziello
Keyword(s):  
General Relativity ◽  
Quantum Interference ◽  
Relativistic Effects ◽  
Newtonian Potential ◽  
Alternative Theories Of Gravity ◽  
Gravitational Fields ◽  
Decoherence Rate ◽  
Relativistic Regime ◽  
Theories Of Gravity ◽  
To Come

AbstractIn this paper, we study the phenomenon of quantum interference in the presence of external gravitational fields described by alternative theories of gravity. We analyze both non-relativistic and relativistic effects induced by the underlying curved background on a superposed quantum system. In the non-relativistic regime, it is possible to come across a gravitational counterpart of the Bohm–Aharonov effect, which results in a phase shift proportional to the derivative of the modified Newtonian potential. On the other hand, beyond the Newtonian approximation, the relativistic nature of gravity plays a crucial rôle. Indeed, the existence of a gravitational time dilation between the two arms of the interferometer causes a loss of coherence that is in principle observable in quantum interference patterns. We work in the context of generalized quadratic theories of gravity to compare their physical predictions with the analogous outcomes in general relativity. In so doing, we show that the decoherence rate strongly depends on the gravitational model under investigation, which means that this approach turns out to be a promising test bench to probe and discriminate among all the extensions of Einstein’s theory in future experiments.

scholarly journals Testing the Vainshtein mechanism using stars and galaxies

2015 ◽  
Vol 24 (12) ◽  
pp. 1544021 ◽  
Author(s):  
Jeremy Sakstein ◽  
Kazuya Koyama
Keyword(s):  
General Relativity ◽  
Solar System ◽  
Main Sequence ◽  
Alternative Theories Of Gravity ◽  
The Novel ◽  
Main Sequence Stars ◽  
Cosmic Expansion ◽  
Astrophysical Objects ◽  
Theories Of Gravity ◽  
Alternative Theories

The Vainshtein mechanism is of paramount importance in many alternative theories of gravity. It hides deviations from general relativity (GR) in the solar system while allowing them to drive the acceleration of the cosmic expansion. Recently, a class of theories have emerged where the mechanism is broken inside astrophysical objects. In this essay, we look for novel probes of these theories by deriving the modified properties of stars and galaxies. We show that main-sequence stars are colder, less luminous and more ephemeral than GR predicts. Furthermore, the circular velocities of objects orbiting inside galaxies are slower and the lensing of light is weaker. We discuss the prospects for testing these theories using the novel phenomena presented here in light of current astrophysical surveys.

scholarly journals Testing theories of gravity and supergravity with inflation and observations of the cosmic microwave background

2017 ◽  
Vol 26 (13) ◽  
pp. 1730023 ◽  
Author(s):  
G. K. Chakravarty ◽  
S. Mohanty ◽  
G. Lambiase
Keyword(s):  
General Relativity ◽  
Cosmic Microwave Background ◽  
Cold Dark Matter ◽  
Background Radiation ◽  
Accelerated Expansion ◽  
Microwave Background ◽  
Microwave Background Radiation ◽  
Theories Of Gravity ◽  
The Universe ◽  
Einstein’S General Relativity

Cosmological and astrophysical observations lead to the emerging picture of a universe that is spatially flat and presently undertaking an accelerated expansion. The observations supporting this picture come from a range of measurements encompassing estimates of galaxy cluster masses, the Hubble diagram derived from type-Ia supernovae observations, the measurements of Cosmic Microwave Background radiation anisotropies, etc. The present accelerated expansion of the universe can be explained by admitting the existence of a cosmic fluid, with negative pressure. In the simplest scenario, this unknown component of the universe, the Dark Energy, is represented by the cosmological constant ([Formula: see text]), and accounts for about 70% of the global energy budget of the universe. The remaining 30% consist of a small fraction of baryons (4%) with the rest being Cold Dark Matter (CDM). The Lambda Cold Dark Matter ([Formula: see text]CDM) model, i.e. General Relativity with cosmological constant, is in good agreement with observations. It can be assumed as the first step towards a new standard cosmological model. However, despite the satisfying agreement with observations, the [Formula: see text]CDM model presents lack of congruence and shortcomings and therefore theories beyond Einstein’s General Relativity are called for. Many extensions of Einstein’s theory of gravity have been studied and proposed with various motivations like the quest for a quantum theory of gravity to extensions of anomalies in observations at the solar system, galactic and cosmological scales. These extensions include adding higher powers of Ricci curvature [Formula: see text], coupling the Ricci curvature with scalar fields and generalized functions of [Formula: see text]. In addition, when viewed from the perspective of Supergravity (SUGRA), many of these theories may originate from the same SUGRA theory, but interpreted in different frames. SUGRA therefore serves as a good framework for organizing and generalizing theories of gravity beyond General Relativity. All these theories when applied to inflation (a rapid expansion of early universe in which primordial gravitational waves might be generated and might still be detectable by the imprint they left or by the ripples that persist today) can have distinct signatures in the Cosmic Microwave Background radiation temperature and polarization anisotropies. We give a review of [Formula: see text]CDM cosmology and survey the theories of gravity beyond Einstein’s General Relativity, specially which arise from SUGRA, and study the consequences of these theories in the context of inflation and put bounds on the theories and the parameters therein from the observational experiments like PLANCK, Keck/BICEP, etc. The possibility of testing these theories in the near future in CMB observations and new data coming from colliders like the LHC, provides an unique opportunity for constructing verifiable models of particle physics and General Relativity.

scholarly journals Anisotropic cosmological dynamics in f(T) gravity in the presence of a perfect fluid

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
Maria A. Skugoreva ◽  
Alexey V. Toporensky
Keyword(s):  
General Relativity ◽  
Equation Of State ◽  
Perfect Fluid ◽  
Matter Content ◽  
Cosmological Evolution ◽  
Anisotropic Universe ◽  
Anisotropic Solution ◽  
Cosmological Singularity ◽  
Hubble Parameters ◽  
The Universe

Abstract We consider the cosmological evolution of a flat anisotropic Universe in f(T) gravity in the presence of a perfect fluid. It is shown that the matter content of the Universe has a significant impact of the nature of a cosmological singularity in the model studied. Depending on the parameters of the f(T) function and the equation of state of the perfect fluid in question the well-known Kasner regime of general relativity can be replaced by a new anisotropic solution, or by an isotropic regime, or the cosmological singularity changes its nature to a non-standard one with a finite values of Hubble parameters. Six possible scenarios of the cosmological evolution for the model studied have been found numerically.

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