普朗克2015数据下的对数修正F(R)重力理论

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"根据普朗克2015年对数校正的F（R）重力" 这篇研究文章发表在《Physics Letters B》751期（2015年），由J.Sadeghi和H.Farahani共同撰写。该论文探讨了一种修改后的重力理论，即F(R)重力理论，其拉格朗日密度表达式为£= R + αR^2 + βR^2ln⁡(βR)，其中α和β是理论中的常数。F(R)重力理论是广义相对论的扩展，旨在解释宇宙学中的某些现象，如暗物质和暗能量。文章的核心内容包括以下几个方面： 1. 恒定曲率解：作者们通过分析得到了理论中的恒定曲率解。在F(R)重力理论中，这种解可以对应于不同宇宙阶段的背景几何，例如平坦、开放或闭合的宇宙模型。这些解对于理解宇宙的演化至关重要。 2. 标量势：他们进一步求得了引力场的标量势。标量势是描述引力场强度的一个重要量，它在F(R)重力理论中起着关键作用，因为它与宇宙的加速膨胀有关。 3. 爱因斯坦框架下的质量平方：在爱因斯坦框架下，作者计算了标量的质量平方。这个计算对于理解标量场如何影响宇宙的动态以及如何与观测数据相符合是必要的。 4. 宇宙学参数：基于普朗克2015年的最新观测数据，研究人员确定了相应的宇宙学参数。这些参数包括哈勃常数、宇宙的年龄、暗物质和暗能量的比例等，它们对于构建符合观测的宇宙模型至关重要。 5. 理论的临界点和稳定性分析：文章还分析了新提出的修正重力理论的临界点和稳定性。这涉及到对理论动力学系统的深入研究，以确保模型在物理上是合理的，并且能够稳定地描述宇宙的演化。 6. 对数校正的重要性：作者强调，引入对数校正对于构建一个成功的模型是必要的。这表明对数项在修正广义相对论并使其与普朗克数据一致时起着关键作用，可能是解决现有理论与观测之间不匹配问题的一种策略。这篇论文为理解宇宙的结构和演化提供了一个新的视角，特别是通过引入对数校正的F(R)重力理论，它可能有助于更好地解释暗能量和宇宙加速膨胀的现象。同时，这一理论的稳定性分析和与普朗克数据的比较，为未来的研究提供了坚实的基础。由于是开放访问的文章，它允许全球的科学家和研究者自由获取和评估这些研究成果。

Physics Letters B 751 (2015) 89–95

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Logarithmic corrected F (R) gravity in the light of Planck 2015

J. Sadeghi, H. Farahani

∗

Department of Physics, University of Mazandaran, P.O. Box 47416-95447, Babolsar, Iran

a r t i c l e i n f o a b s t r a c t

Article history:

Received

31 August 2015

Received

in revised form 7 October 2015

Accepted

7 October 2015

Available

online 20 October 2015

Editor:

J. Hisano

Keywords:

Modiﬁed

gravity

Plank

data

Einstein’s

frame

In this Letter, we consider the theory of F (R) gravity with the Lagrangian density £ = R + α R

ln β R. We obtain the constant curvature solutions and ﬁnd the scalar potential of the gravitational

ﬁeld. We also obtain the mass squared of a scalaron in the Einstein’s frame. We ﬁnd cosmological

parameters corresponding to the recent Plank 2015 results. Finally, we analyze the critical points and

stability of the new modiﬁed theory of gravity and ﬁnd that logarithmic correction is necessary to have

successful model.

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

1. Introduction

Recent astrophysical observations clarify the accelerated expan-

sion

of universe [1–3], which may be described by dark energy

scenario. In that case, there are several dark energy models, the

simplest one is the cosmological constant, however it is not a dy-

namical

model, so there are another alternative theories such as

quintessence [4–9], phantom [10–16], and quintom [17–19] mod-

els,

or holographic dark energy proposal [20–23]. Moreover, there

are interesting models to describe the dark energy such as Chaply-

gin

gas [24–42].

Modiﬁcation

of the Einstein–Hilbert (EH) action through the

Ricci scalar can describe inﬂation and also present accelerated ex-

pansion

of universe. This called F (R) gravity model, so there are

several ways to construct a F (R) gravity models [43–46]. In this

paper we consider the particular case of the F (R) gravity model

where the Ricci scalar replaced by a new function,

F (R) = R +αR

+β R

ln β R, (1.1)

where β>0is the parameter with the squared length dimension

and also α > 0. This model can describe the universe evolution

without introducing the dark energy [47], where the cosmic accel-

eration

exists due to the modiﬁed gravity. So, F (R) gravity models

can be replaced to the cosmological constant model.

The

function given by (1.1) without logarithmic correction

(β =0) has been studied by [48,49] which is applicable to a neu-

Corresponding author.

E-mail

addresses: pouriya@ipm.ir (J. Sadeghi), h.farahani@umz.ac.ir (H. Farahani).

tron star with a strong magnetic ﬁeld [50]. In order to consider

effect of gluons in curved space–time, the logarithmic correction in

(1.1) proposed by [51]. In the Ref. [51] a phenomenological model

based on the equation (1.1) proposed. Motivated by this model, we

would like to use relation (1.1) to study some cosmological param-

eters

in the light of new data of Planck 2015.

Initial

idea of the F (R) gravity models successfully examined by

Refs. [52–54]. Then, several models of F (R) gravity introduced in

the literature [55–61]. These are indeed phenomenological mod-

els

which describe evolution of universe. The Minkowski metric

μν

= diag(−1, 1, 1, 1) and c =

h = 1are used in the initial F (R)

gravity model [62]. Now, we would like to use logarithmic cor-

rected

F (R) model given by the equation (1.1) and exam cosmo-

logical

consequences of the model using recent data of Planck [63].

This

paper is organized as follows. In Section 2, we introduce

the model, then we study constant curvature condition in Sec-

tion 3.

In Section 4 we obtain the form of the scalar tensor. Cos-

mological

parameters like tensor to scalar ratio are obtained in

Section 5. Critical points and stability analyzed in Section 6. Fi-

nally,

in Section 7 we give conclusion.

2. The model

We begin with the equation (1.1) to modify the Ricci scalar R in

the EH action. The function F (R) satisﬁes the conditions F (0) = 0,

corresponding to the ﬂat space–time without cosmological con-

stant.

Thus, the action in the Jordan frame becomes

S =



√

−g£ =



√

−g



2κ

F (R) +£



(2.1)

http://dx.doi.org/10.1016/j.physletb.2015.10.020

0370-2693/

SCOAP

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