# Modified gravity

#### wolram

Gold Member
http://arxiv.org/abs/astro-ph/0506692

Title: Cosmological expansion and the uniqueness of gravitational action
Authors: T. Multamaki, I. Vilja

Modified theories of gravity have recently been studied by several authors as possibly viable alternatives to the cosmological concordance model. Such theories attempt to explain the accelerating expansion of the universe by changing the theory of gravity, instead of introducing dark energy. In particular, a class of models based on higher order curvature invariants, so-called $f(R)$ gravity models, has drawn attention. In this letter we show that within this framework, the expansion history of the universe does not uniquely determine the form of the gravitational action and it can be radically different from the standard Einstein-Hilbert action. We demonstrate that for any barotropic fluid, there always exists a class of $f(R)$ models that will have exactly the same expansion history as that arising from the Einstein-Hilbert action. We explicitly show how one can extend the Einstein-Hilbert action by constructing a $f(R)$ theory that is equivalent on the classical level. Due to the classical equivalence between $f(R)$ theories and Einstein-Hilbert gravity with an extra scalar field, one can also hence construct equivalent scalar-tensor theories with standard expansion.

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#### Garth

Gold Member
Any such theory would have to be testable in the solar system as well as explain: the distant SN Ia observations, the times of structure and object formation in the early universe and the spatial flatness (actually conformal flatness) interpreted from the CMB WMAP data.

But then if it can do all this it would be preferable to the extra 'epicycle' that is DE.

Garth

#### Chronos

Gold Member
From the paper "We demonstrate that for any barotropic fluid, there always exists a class of $f(R)$ models that will have exactly the same expansion history as that arising from the Einstein-Hilbert action." While true, that assertion is meaningless.

#### ohwilleke

Gold Member
I wouldn't say it is meaningless. One of the arguments for GR is that other approaches fail to explain the expansion history of the universe. This paper is an existence proof, showing that not just one other, but an entire class of other gravitational functions can produce the same result at the cosmological level. This then allows anyone using that class of functions as a basis to know that it will be cosmologically identical to GR.

It is a bit like a paper which shows that any Lagrangian based theory will conform to a host of common conservation laws, or that any tensor based theory will, as a matter of form, be invariant in the face of a coordinate system change.

#### Chronos

Gold Member
But I think that is an appeal to extra dimensions. And I object. Once you invoke extra dimensions, the whole thing seems to spiral out of control. I don't necessarily object to extra dimensions, but I insist they converge at the 3 + 1 level.

#### wolram

Gold Member
Chronos said:
But I think that is an appeal to extra dimensions. And I object. Once you invoke extra dimensions, the whole thing seems to spiral out of control. I don't necessarily object to extra dimensions, but I insist they converge at the 3 + 1 level.
I like your ideals Chronos, all this extra dimension and multiverse speculation
seems like desperation to me.

#### bigles

Embeding and projecting

Chronos said:
I don't necessarily object to extra dimensions, but I insist they converge at the 3 + 1 level.
I don't object to Hilbertspaces with an infinite number of dimensions, as long as it is possible to project all physical stuff to euclidian space-time.

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