scholarly journals ON ANALYTICAL SOLUTIONS OF f(R) MODIFIED GRAVITY THEORIES IN FLRW COSMOLOGIES

2013 ◽  
Vol 22 (02) ◽  
pp. 1350006 ◽  
Author(s):  
SILVIJE DOMAZET ◽  
VOJA RADOVANOVIĆ ◽  
MARKO SIMONOVIĆ ◽  
HRVOJE ŠTEFANČIĆ
Keyword(s):  
Power Law ◽  
Analytical Solutions ◽  
Modified Gravity ◽  
Cosmic Time ◽  
Equation Of Motion ◽  
Scale Factor ◽  
Ricci Scalar ◽  
Late Time ◽  
Modified Gravity Theories ◽  
Functional Forms

A novel analytical method for f(R) modified theories without matter in Friedmann–Lemaitre–Robertson–Walker (FLRW) spacetimes is introduced. The equation of motion for the scale factor in terms of cosmic time is reduced to the equation for the evolution of the Ricci scalar R with the Hubble parameter H. The solution of equation of motion for actions of the form of power law in Ricci scalar R is presented with a detailed elaboration of the action quadratic in R. The reverse use of the introduced method is exemplified in finding functional forms f(R), which leads to specified scale factor functions. The analytical solutions are corroborated by numerical calculations with excellent agreement. Possible further applications to the phases of inflationary expansion and late-time acceleration as well as f(R) theories with radiation are outlined.

scholarly journals POWER-LAWS f(R) THEORIES ARE COSMOLOGICALLY UNACCEPTABLE

2007 ◽  
Vol 16 (10) ◽  
pp. 1555-1561 ◽  
Author(s):  
LUCA AMENDOLA ◽  
DAVID POLARSKI ◽  
SHINJI TSUJIKAWA
Keyword(s):  
Dark Energy ◽  
Recent Work ◽  
Modified Gravity ◽  
Cosmic Time ◽  
Power Laws ◽  
Scale Factor ◽  
Late Time ◽  
Cosmic Expansion ◽  
Late Time Acceleration ◽  
Energy Models

In a recent paper,1 we have shown that f(R) = R + μRn modified gravity dark energy models are not cosmologically viable because during the matter era that precedes the accelerated stage the cosmic expansion is given by a ~ t1/2 rather than a ~ t2/3, where a is a scale factor and t is the cosmic time. A recent work by Capozziello et al.2 criticized our results presenting some apparent counter-examples to our claim in f(R) = μRn models. We show here that those particular Rn models can produce an expansion as a ~ t2/3 but this does not connect to a late-time acceleration. Hence, though acceptable f(R) dark energy models might exist, the Rn models presented in Capozziello et al. are not cosmologically viable, confirming our previous results in Ref. 1.

Power law expansion of the early universe for a V (a) = kan potential

2018 ◽  
Vol 33 (01) ◽  
pp. 1850005
Author(s):  
Augusto S. Freitas
Keyword(s):  
Early Universe ◽  
Power Law ◽  
Analytical Solutions ◽  
Scale Factor ◽  
Rigorous Proof ◽  
Exponential Expansion ◽  
True Vacuum ◽  
Classical Potential ◽  
The Universe

In a recent paper, He, Gao and Cai [Phys. Rev. D 89, 083510 (2014)], found a rigorous proof, based on analytical solutions of the Wheeler–DeWitt (WDWE) equation, of the spontaneous creation of the universe from nothing. The solutions were obtained from a classical potential [Formula: see text], where [Formula: see text] is the scale factor. In this paper, we present a complementary (to that of He, Gao and Cai) solution to the WDWE equation with [Formula: see text]. I have found an exponential expansion of the true vacuum bubble for all scenarios. In all scenarios, we found a power law behavior of the scale factor result which is in agreement with another studies.

scholarly journals Cosmology with Variable G and Nonlinear Electrodynamics

2020 ◽  
Author(s):  
Gabriel W. Joseph ◽  
Ali Övgün
Keyword(s):  
Power Law ◽  
Speed Of Sound ◽  
Gravitational Constant ◽  
Cosmic Time ◽  
Scale Factor ◽  
Fine Tuning ◽  
Nonlinear Electrodynamics ◽  
The Stability ◽  
The Universe ◽  
Constants Of Nature

In a bid to resolve lingering problems in cosmology, more focus is being tilted towards cosmological models in which physical constants of nature are not necessarily real constants, but varying with cosmic time. In this paper we have study cosmology in nonlinear electrodynamics with the Newton's gravitational constant $G$ not a constant but vary in form of power-law of the scale factor of the universe. The evolution of the scale factor $a (t)$ is studied in this model which depends on nonlinear electrodynamics fine tuning term of $\alpha$. Then we check the stability of the model using the speed of sound.

scholarly journals Ricci–Gauss–Bonnet holographic dark energy in Chern–Simons modified gravity: A flat FLRW quintessence-dominated universe

2019 ◽  
Vol 35 (05) ◽  
pp. 2050007 ◽  
Author(s):  
Nasr Ahmed
Keyword(s):  
Dark Energy ◽  
Modified Gravity ◽  
Holographic Dark Energy ◽  
Cosmic Time ◽  
Early Time ◽  
State Parameter ◽  
Late Time ◽  
Equation Of State Parameter ◽  
Chern Simons ◽  
Far Future

We discuss the recently suggested Ricci–Gauss–Bonnet holographic dark energy in Chern–Simons modified gravity. We have tested some general forms of the scale factor [Formula: see text], and used two physically reasonable forms which have been proved to be consistent with observations. Both solutions predict a sign flipping in the evolution of cosmic pressure which is positive during the early-time deceleration and negative during the late-time acceleration. This sign flipping in the evolution of cosmic pressure helps in explaining the cosmic deceleration–acceleration transition, and it has appeared in other cosmological models in different contexts. However, this work shows a pressure singularity which needs to be explained. The evolution of the equation of state parameter [Formula: see text] shows the same asymptotic behavior for both solutions indicating a quintessence-dominated universe in the far future. We also note that [Formula: see text] goes to negative values (leaving the decelerating dust-dominated era at [Formula: see text]) at exactly the same time the pressure becomes negative. Again, there is another singularity in the behavior of [Formula: see text] which happens at the same cosmic time of the pressure singularity.

Scale factor — Cosmic time relation and occurrences of future cosmic singularities with different redshift parametrizations of dark energy EoS-s

2019 ◽  
Vol 34 (28) ◽  
pp. 1950228
Author(s):  
Swetalina Bhowmik ◽  
Ritabrata Biswas
Keyword(s):  
Dark Energy ◽  
Equation Of State ◽  
Cosmic Time ◽  
Scale Factor ◽  
Late Time ◽  
Expanding Universe ◽  
Unknown Parameters ◽  
Time Relation

While modeling our late time cosmically accelerated universe, it is popular to involve different dark energy (DE) models, the equation of state (EoS) of which can be taken as a function of the redshift and some unknown parameters. Barboza and Alcaniz have proposed one such kind of DE EoS model. We use some new parametrizations like Feng, Shen, Li, Li I and II and Polynomial parametrizations to get more accurate concepts about the fate of our expanding universe. We try to find how the hypothesis of the fate of our universe behaves in the above background of DE models. Possibilities of occurrences of future cosmic singularities are studied.

scholarly journals A Dark Energy Model with Higher Order Derivatives of H in the f(R,T) Modified Gravity Model

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Antonio Pasqua ◽  
Surajit Chattopadhyay ◽  
Ratbay Myrzakulov
Keyword(s):  
Dark Energy ◽  
Gravity Model ◽  
Modified Gravity ◽  
Hubble Parameter ◽  
Time Derivative ◽  
Cosmic Time ◽  
Late Time ◽  
Eos Parameter ◽  
Curvature And Torsion ◽  
The Universe

We consider a model of dark energy (DE) which contains three terms (one proportional to the squared Hubble parameter, one to the first derivative, and one to the second derivative with respect to the cosmic time of the Hubble parameter) in the light of the f(R,T)=μR+νT modified gravity model, with μ and ν being two constant parameters. R and T represent the curvature and torsion scalars, respectively. We found that the Hubble parameter exhibits a decaying behavior until redshifts z≈-0.5 (when it starts to increase) and the time derivative of the Hubble parameter goes from negative to positive values for different redshifts. The equation of state (EoS) parameter of DE and the effective EoS parameter exhibit a transition from ω<-1 to ω>-1 (showing a quintom-like behavior). We also found that the model considered can attain the late-time accelerated phase of the universe. Using the statefinder parameters r and s, we derived that the studied model can attain the ΛCDM phase of the universe and can interpolate between dust and ΛCDM phase of the universe. Finally, studying the squared speed of sound vs2, we found that the considered model is classically stable in the earlier stage of the universe but classically unstable in the current stage.

scholarly journals Late time transition in the evolution of the Universe

2021 ◽  
Author(s):  
Ekrem Aydiner ◽  
Isil Basaran Oz ◽  
Tekin Dereli ◽  
Mustafa Sarisaman
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Power Law ◽  
Numerical Solutions ◽  
Scale Factor ◽  
Late Time ◽  
Transition Problem ◽  
Exponential Expansion ◽  
Expansion Of The Universe ◽  
The Universe

Abstract The late time crossover from a power-law to an exponential expansion of the Universe evolution is the major problem in today’s physical cosmology. Unless this critical transition problem is solved, it is not possible to reach a holistic theory of cosmology. In this study, we propose a simple model in the FLRW framework, where dark matter and dark energy interact through a potential. We analytically solve this model and obtain scale factor a(t) from the presented model. Mainly, employing numerical solutions we show that the scale parameter has a hybrid form which includes power and exponential terms. The numerical results clearly show that there is a time crossover tc in the scale factor a(t) curve, which indicates the transition from the power-law to the exponential expansion of the Universe. We fit these unscaled curves and obtain that scale factor behaves as a(t) ∝ t2/3 below t ≤ tc, and as a(t) ∝ exp(H0t) with H0 = 0.4 and H0 = 0.3 for the relatively weak and strong interactions above t > tc, respectively. It is the first time that we explicitly obtain a hybrid scale factor incorporating the power and exponential terms as a(t) ∝ t2/3eH0t . We conclude that the presented model can solve the late time transition problem of the Universe based on dark matter and dark energy interaction. Additionally, we numerically obtain other kinematic parameters depending upon the scale factor. We discuss the limit behaviors of all relevant cosmological parameters. Our results are completely in good agreement with observational data. Finally, we state that this work makes essential steps towards solving a critical outstanding problem of the cosmology, and has a potential to creates a paradigm for future studies in this field.

scholarly journals de Sitter and power-law solutions in some models of modified gravity

2016 ◽  
Vol 31 (38) ◽  
pp. 1650221 ◽  
Author(s):  
Yi Zhong ◽  
Emilio Elizalde
Keyword(s):  
Power Law ◽  
Modified Gravity ◽  
Scale Factor ◽  
Accurate Description ◽  
Nonlocal Term ◽  
De Sitter ◽  
New Approaches ◽  
Power Scale ◽  
Mimetic Gravity

Inspired by some recent works of Lovelock Brans–Dicke (BD) gravity and mimetic gravity, cosmology solutions in extensions of these two modified gravities are investigated. A nonlocal term is added to the Lovelock BD action and Gauss–Bonnet (GB) terms to the mimetic action, correspondingly. de Sitter and power scale factor solutions are then obtained in both theories. They can provide natural new approaches to a more accurate description of the unverse evolution.

scholarly journals Late time transition in the evolution of the Universe

2021 ◽  
Author(s):  
EKREM AYDINER ◽  
Isil Oz ◽  
Tekin Dereli ◽  
Mustafa Sarisaman
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Power Law ◽  
Numerical Solutions ◽  
Scale Factor ◽  
Late Time ◽  
Transition Problem ◽  
Exponential Expansion ◽  
Expansion Of The Universe ◽  
The Universe

Abstract The late time crossover from a power-law to an exponential expansion of the Universe evolution is the major problem in today’s physical cosmology. Unless this critical transition problem is solved, it is not possible to reach a holistic theory of cosmology. In this study, we propose a simple model in the FLRW framework, where dark matter and dark energy interact through a potential. We analytically solve this model and obtain scale factor a(t) from the presented model. Mainly, employing numerical solutions we show that the scale parameter has a hybrid form which includes power and exponential terms. The numerical results clearly show that there is a time crossover tc in the scale factor a(t) curve, which indicates the transition from the power-law to the exponential expansion of the Universe. We fit these unscaled curves and obtain that scale factor behaves as a(t) ∝ t 2/3 below t ≤ tc, and as a(t) ∝ exp(H0t) with H0 = 0.4 and H0 = 0.3 for the relatively weak and strong interactions above t > tc, respectively. It is the first time that we explicitly obtain a hybrid scale factor incorporating the power and exponential terms as a(t) ∝ t 2/3 e H0t . We conclude that the presented model can solve the late time transition problem of the Universe based on dark matter and dark energy interaction. Additionally, we numerically obtain other kinematic parameters depending upon the scale factor. We discuss the limit behaviors of all relevant cosmological parameters. Our results are completely in good agreement with observational data. Finally, we state that this work makes essential steps towards solving a critical outstanding problem of the cosmology, and has a potential to creates a paradigm for future studies in this field.

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