Questions tagged [modified-gravity]

A set of theories that attempt to take the basics of general relativity, and extend it in such a way that it solves various problems. This applies to Milgrom's MOND proposal, but also includes such other things as Einstein-Cartan theory, Brans-Dicke theory, and $f(R)$ gravity.

Filter by
Sorted by
Tagged with
0 votes
1 answer
33 views

Obtaining the KG equation from Action

After solving the field equation for $$S = \int \sqrt{-g}dx^4[f(\phi)R + h(\phi)g^{\mu \nu}\nabla_{\mu}\phi\nabla_{\nu}\phi - V(\phi)]$$ I have obtained $$2h\square \phi + \frac{\partial h}{\partial \...
user avatar
  • 2,824
0 votes
2 answers
48 views

Variation for the Canonical Scalar Field in $f(\phi)R$

I am trying to find the Field equation for $$S = \int \sqrt{-g}dx^4[f(\phi)R + h(\phi)g^{\mu \nu}\nabla_{\mu}\phi\nabla_{\nu}\phi - V(\phi)$$ but I could not take the variation of $$\delta(\sqrt{-g}h(\...
user avatar
  • 2,824
0 votes
1 answer
65 views

State of the art on Modified gravity : going beyond the 2nd order differential equations, diffeomorphism invariance breaking, extra degrees of freedom

I am going to do a state of the art on Modified gravity models. I have found a talk that presents the problematic. In particular, it is said the following things : Modifying General Relativity How to ...
user avatar
  • 19.2k
1 vote
1 answer
35 views

Book/Article recommendation about modified gravity (scalar/tensor/scalar-tensor theories)

Is there a book or article that discusses the modified gravity theories scalar/tensor/scalar-tensor (maybe others as well) theories? (Look at this wiki page for a general overview of the theories that ...
0 votes
0 answers
32 views

Problem with field equations in five-dimensional $f(R)$ gravity

I am trying to reproduce the calculations in this paper by Biao Huang, Song Li, and Yongge Ma. The equation of concern is Eq. 9, where the field equation is derived as follows: $$\begin{align} G_{ab}...
user avatar
1 vote
1 answer
106 views

Is Bertrand's Theorem Consistent with GR?

Bertrand's Theorem - Please observe the gif of orbits with different exponents in the denominator. (I couldn't get the image upload feature to work for this) Note, the orbit with a 1.9 exponent ...
user avatar
2 votes
1 answer
95 views

What explains the descrepancy between Asaph Hall's equation for Mercury's precession and GR?

In regard to What is the weight equation through general relativity?, the answer is: $$F=ma=\frac{GMm}{r^2}\frac{1}{\sqrt{1-\frac{2GM}{c^2r}}}.$$ This source provides a different equation: $$f \approx ...
user avatar
4 votes
1 answer
54 views

Does Lorentz invariance imply the impossibility to detect an event horizon from a local experiment?

It appears that it is impossible to detect the event horizon from a local experiment. Is this a consequence that General Relativity always reduces locally to a Lorentz invariant theory? Or in other ...
user avatar
  • 676
5 votes
1 answer
133 views

What’s wrong with this Nordström-like scalar theory of gravity?

I got very perplexed while reading a few papers on the old Nordström theory of relativistic scalar gravity. I would like to know what's wrong with the following, which isn't exactly the same as ...
user avatar
  • 6,696
3 votes
0 answers
62 views

Which geodesics light travels on: metric or affine in Einstein-Cartan theory?

In a generic Lorentzian spacetime solving the Einstein equations since both the metric and affine geodesic coincide this question doesn't arise. But in the Einstein–Cartan theory it is not very ...
user avatar
  • 810
4 votes
1 answer
305 views

Is a vacuum-energy smaller than zero forbidden? Why?

Einstein's Field Equations allow for the derivation of Newton's law and this, together with the velocity profile of the stars within the galaxies and the galaxies within the galaxy clusters, leads to ...
user avatar
3 votes
0 answers
191 views

Does Higher spinor field bend Space-time?

Consider the free massless spin-$n/2$ field in a general curved space-time ($M$, $g$): \begin{equation} \nabla^{AA'}\phi_{\underbrace{AB\cdots L}_n} =0\end{equation}If $\phi_{AB\cdots L}$ has charge $...
user avatar
  • 743
0 votes
0 answers
57 views

Asymptotic behaviour of a non-linear differential equation in Gravitation

I have been recently working on modifications to General Relativity, by adding new curvature terms in the Lagrangian density of the theory. In one of these theories (Einsteinian Cubic Gravity), the ...
user avatar
  • 1
2 votes
1 answer
117 views

Newtonian quantum gravity

Can someone give me reference about Newtonian (non-relativistic) quantum gravity like unifying Newtonian gravity with quantum mechanics?
-1 votes
3 answers
91 views

Newton's Law of Gravitation and dark matter [closed]

Before the days of Einstein the observation that light incident to the Earth's surface appears to be constant no matter whether the transmitter is travelling away from the earth or towards the earth ...
user avatar
  • 9
0 votes
0 answers
32 views

Could quantum vacuum polarization increase GR frame dragging beyond the predicted values and therefore replace DM explanation of galactic rotation? [duplicate]

image source credits:David Butler This anomalous speed rotation distribution of galaxies is today mainly contributed to Dark Matter. However, since a definitive experimental measurement and ...
user avatar
  • 3,025
0 votes
0 answers
41 views

Are quadratic gravity's equations of motion just regular gravity with some minimal length?

So, I came to this while doing some calculations in quadratic gravity with the following action: \begin{equation} S = \int d^4x \sqrt{-g}\left[ \frac{1}{2}m^4+\frac{1}{6}m^2 R +\frac{1}{72}R^2+\frac{1}...
user avatar
1 vote
1 answer
111 views

Graviton propagator in Horndeski theory

Let $\phi$ be a scalar field and $g_{\mu \nu} = \eta_{\mu \nu}+h_{\mu \nu}/M_p$ where $M_p$ is the Planck mass (so we assume we deal with perturbations). Let $\Lambda_2,\Lambda_3$ be energy scales ...
user avatar
1 vote
1 answer
261 views

Feynman rules Horndeski theory

Let $\phi$ be a scalar field and $g_{\mu \nu} = \eta_{\mu \nu}+h_{\mu \nu}/M_p$ where $M_p$ is the Planck mass (so we assume we deal with perturbations). Let $\Lambda_2,\Lambda_3$ be energy scales ...
user avatar
-1 votes
1 answer
81 views

Switch from $AdS$ to $dS$ in quadratic gravity using $f(R)$ trick: problem

I have some difficulties with effective quadratic gravity involving a cosmological constant with the "wrong sign". The following is the setup of my question. Let's assume one has the ...
user avatar
1 vote
0 answers
39 views

Contradictions in articles about renormalizability of Einstein-conformal gravity

Background: In the calculations I've done, I've found an action of the following form: \begin{equation} S=\int d^4x\,\sqrt{-g}\left( \xi^2R+\frac{1}{120}\xi^2C_{\alpha \beta \mu \nu}C^{\alpha \beta \...
user avatar
1 vote
1 answer
170 views

Can Integrating out Dark Matter give Modified Gravity?

I'm sure I misunderstood something obvious, but reading this question, I wondered what philosophically is the difference between modified gravity (like TeVeS, f(R), etc.) and dark matter, if/since we ...
user avatar
  • 222
1 vote
1 answer
140 views

If MOND were true, what would that imply for the geometrical description of gravity as curved spacetime?

As I understand it, Modified Newtonian Dynamics, or MOND (Milgrom M., 1983, ApJ, 270, 365), slightly alters Newton's Law of Gravity by introducing a low acceleration limit below which (for an object ...
user avatar
1 vote
1 answer
84 views

Equations of motion of the metric in Classical Dilaton Gravity

In these lecture notes by Strominger section 3.3 we derive the equations of motion of the Classical Dilaton Gravity action $$ S = \frac{1}{2\pi}\int{d^2x}{\sqrt{-g}e^{-2\phi}\left(R +4 (\nabla\phi)^2+...
user avatar
1 vote
1 answer
55 views

Why are wide binary systems assumed to contain negligible dark matter?

I'm doing a project that simulates wide binaries to do gravity tests, specifically a dark matter vs MOND test. I've come across similar papers, and their justification for using wide binaries for this ...
user avatar
1 vote
0 answers
60 views

Is the Palatini formulation of a gravity theory a metric one?

As far as i know, the Einstein equivalence principle (EEP) is the starting point to explain gravity as a geometric phenomenom. It allows you to link gravity with two geometrical objects: a metric, ...
user avatar
  • 11
0 votes
1 answer
88 views

If MOND requires fixes at LOW accelerations, why don't we see it in table experiments?

MOND is controlled by $\mu=\mu(\frac{a}{a_0})$ and $\mu\rightarrow1$ when $a\rightarrow0$ But on my table $a=0$ so shouldn't I see ...
user avatar
  • 1,586
2 votes
1 answer
61 views

Dimension of operators in modified gravity

I was reading a paper arXiv:1903.06784 where the following action is considered: \begin{equation} S\sim \int d^4x \sqrt{-g}\bigg[M^2_{Pl}R-\frac{1}{2}(\nabla\phi)^2 -\frac{1}{2}\mu^2\phi^2-\frac{1}{2}\...
user avatar
0 votes
0 answers
64 views

Modify Newton's gravity to cure the action at a distance

Take a bunch of particles (can be point particles) at ${\bf{x}}_i(t)$ and of mass $m_i>0$. The gravitational field is defined by the Poisson equation $$ \nabla^2 \Phi({\bf{x}},t) = 4 \pi G \rho({\...
user avatar
  • 2,895
0 votes
1 answer
108 views

Particular behaviour of 'black hole' horizon in modified gravity

When working in a particular theory of modified gravity, one can see that a solution for a spherically symmetric and static puntual mass is given by \begin{equation} ds^2=-B(r)dt^2+A(r)dr^2+r^2d\theta^...
user avatar
1 vote
0 answers
115 views

What properties of MOND differ from Newtonian gravity?

I know of the following properties that set modified Newtonian dynamics (MOND) apart from Newtonian gravity: There is a $1/r$ dependence instead of a $1/r^2$ dependence, at large distances/low ...
user avatar
2 votes
1 answer
107 views

Higgs non-minimal coupling to gravity: Jordan and Einstein frame

In this paper they consider the Higgs non-minimally coupled to the Ricci scalar. I am trying to recalculate the steps from equation (5) until equation (10). Let's start with (5): $$\int d^4x\sqrt{-g} \...
user avatar
0 votes
1 answer
73 views

A rapid question on $f(R)$ gravity

Is it possible to construct a $f(R)$ where, $$f(R) = \alpha R \tag{1} ?$$ I'm asking this for two reasons: $1)$ I'm quite a freshman on modified theories of gravity and $2)$ Most of the times I see ...
user avatar
  • 2,679
4 votes
0 answers
100 views

How robust is this 2020 measurement of the external field effect (EFE) in MOND?

There's a paper from a few months ago that claims to have measured this unique Modified Newtonian Dynamics (MOND) effect at high significance. The result seems very interesting: The effect is unique ...
user avatar
  • 16.4k
0 votes
2 answers
412 views

How is the External Field Effect in MOND conceptually distinct from Newtonian gravity and GR?

I’m trying to understand the External Field Effect (EFE) in Modified Newtonian Dynamics (MOND) and how it is conceptually distinct from GR and Newtonian gravity. More specifically, the descriptions I ...
user avatar
  • 147
0 votes
0 answers
53 views

Books about the development/history of gravitational theory

I am looking for a book about the history of gravitational theory. It should obviously include discussions of Newton, Einstein, and their theories, and hopefully it would include the work of other ...
1 vote
2 answers
120 views

Why can't Dark Matter be curvature without a proximal mass source? [closed]

I don't understand why Dark Matter or MOND/"gravity works different on bigger scales" are the only options to explain the observational data. Why can't it just be curvature without a "...
user avatar
1 vote
0 answers
99 views

Obtaining General Relativity

Considering the action given in the following post:Induced gravitation action under what conditions does GR originate from this induced gravitation model? Also, what can we say about the cosmological ...
user avatar
7 votes
0 answers
99 views

Propagator in Brans-Dicke Gravity

Consider an action of the form $$ S = -\frac{2}{\kappa^2}\int d^4x\sqrt{-g}~\left(\phi R + \phi\mathcal{L}_{matter}\right). $$ Expanding this to second order in $h_{\mu\nu}$ and including a harmonic ...
user avatar
  • 2,227
1 vote
0 answers
44 views

Decoupling higher order actions

I’m dealing with non-minimally coupling Quadratic gravity in the weak field limit, and as a result of the perturbation $g_{\mu\nu}= \eta_{\mu\nu} +h_{\mu\nu}$ I get some kinetic term mixing. On doing ...
user avatar
1 vote
1 answer
83 views

Induced gravitation action

Considering the action for induced gravity: $$S=\int d^4x\sqrt{-g}\left(\epsilon\phi^2 R-\frac{1}{2}(\partial\phi)^2+V(\phi)\right).$$ I was trying to get the metric field equations by doing the usual ...
user avatar
2 votes
1 answer
250 views

Metric field equations for the Jordan-Brans-Dicke action

Considering the Jordan-Brans-Dicke action: $$S=\int d^4x\sqrt{-g}\left(\phi R+\frac\omega\phi(\partial\phi)^2+\mathfrak{L_{m}}(\psi)\right).$$ I was trying to get the metric field equations by varying ...
user avatar
1 vote
1 answer
123 views

$R=0$ solution in field equations

I am dealing with some General Relativity extensions and I am not sure about my knowledge in basic GR since I am having some weird troubles with what I think are basic concepts. As far as I know, if ...
user avatar
1 vote
1 answer
154 views

Black Holes in Higher Derivative Gravity

It is well known that Einstein Theory of General Relativity has pathological solutions, called black holes, where the theory fails at some point and gives us infinite values. In order to solve this ...
user avatar
1 vote
1 answer
90 views

Squaring the Einstein-Hilbert action - how much damage can a simple squaring do?

I am interested in understanding the consequences of squaring the Einstein Hilbert action: $$ S=\int \sqrt{\left( \left(R\sqrt{|\det g_{\mu\nu}|} \right)^2 + L_m \right)}d^4x $$ The field equations ...
user avatar
  • 1,372
2 votes
2 answers
153 views

If space is expanding, what is the effect on $1/r^2$?

Space is expanding, and this effect can be only detected at large scales, on the scale of galaxies and larger. If space is expanding, the expression $1/r^2$ for the law of gravity will be modified. ...
user avatar
3 votes
1 answer
183 views

Unimodular gravity and Lovelock theorem

I was reading about Unimodular gravity, this is a modified theory of gravity that postulates that the gravity is only invariant under volume preserving diffeomorphism. So it breaks the full ...
user avatar
  • 419
7 votes
3 answers
144 views

Where is the wiggle room in current gravity theories?

As far as I know, General Relativity has long since been proved experimentally to every qualified person's entire satisfaction, and modern technology such as GPS relies on its accurate predictions. ...
user avatar
1 vote
1 answer
57 views

Is there any free utility/software to generates and numerically solve the field equation for modified gravity $f(R)$

I'm looking for a free software (preferred to run under Windows) that can generate the gravity field equations for a given $f(R)$ model in modified gravity. I used Maxima to calculate a few terms, ...
3 votes
1 answer
135 views

How do you know what is the fate of the universe in a modified theory of gravity?

Usually when you talk about the final stage of the universe you assume that $\Lambda CDM$ is the correct cosmological model and with that you can analyze what could happen for different values of $\...
user avatar
  • 419