# Does loop quantum cosmology replace the big rip singularity by a non-singular bounce?

## Abstract

It is stated that holonomy corrections in loop quantum cosmology introduce a modification in Friedmann's equation which prevent the big rip singularity. Recently in [1] it has been proved that this modified Friedmann equation is obtained in an inconsistent way, what means that the results deduced from it, in particular the big rip singularity avoidance, are not justified. The problem is that holonomy corrections modify the gravitational part of the Hamiltonian of the system leading, after Legendre's transformation, to a non covariant Lagrangian which is in contradiction with one of the main principles of General Relativity. A more consistent way to deal with the big rip singularity avoidance is to disregard modification in the gravitational part of the Hamiltonian, and only consider inverse volume effects [2]. In this case we will see that, not like the big bang singularity, the big rip singularity survives in loop quantum cosmology. Another way to deal with the big rip avoidance is to take into account geometric quantum effects given by the the Wheeler-De Witt equation. In that case, even though the wave packets spread, the expectation values satisfy the same equations as their classical analogues. Then, following the viewpoint adopted in loop quantummore »

- Authors:

- Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Diagonal 647, 08028 Barcelona (Spain)

- Publication Date:

- OSTI Identifier:
- 22279822

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2012; Journal Issue: 11; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; CORRECTIONS; COSMOLOGICAL MODELS; COSMOLOGY; EVOLUTION; EXPECTATION VALUE; FIELD EQUATIONS; GENERAL RELATIVITY THEORY; GRAVITATION; HAMILTONIANS; LAGRANGIAN FUNCTION; SEMICLASSICAL APPROXIMATION; SINGULARITY; TRANSFORMATIONS; UNIVERSE; WAVE PACKETS

### Citation Formats

```
Haro, Jaume de, E-mail: jaime.haro@upc.edu.
```*Does loop quantum cosmology replace the big rip singularity by a non-singular bounce?*. United States: N. p., 2012.
Web. doi:10.1088/1475-7516/2012/11/037.

```
Haro, Jaume de, E-mail: jaime.haro@upc.edu.
```*Does loop quantum cosmology replace the big rip singularity by a non-singular bounce?*. United States. doi:10.1088/1475-7516/2012/11/037.

```
Haro, Jaume de, E-mail: jaime.haro@upc.edu. Thu .
"Does loop quantum cosmology replace the big rip singularity by a non-singular bounce?". United States. doi:10.1088/1475-7516/2012/11/037.
```

```
@article{osti_22279822,
```

title = {Does loop quantum cosmology replace the big rip singularity by a non-singular bounce?},

author = {Haro, Jaume de, E-mail: jaime.haro@upc.edu},

abstractNote = {It is stated that holonomy corrections in loop quantum cosmology introduce a modification in Friedmann's equation which prevent the big rip singularity. Recently in [1] it has been proved that this modified Friedmann equation is obtained in an inconsistent way, what means that the results deduced from it, in particular the big rip singularity avoidance, are not justified. The problem is that holonomy corrections modify the gravitational part of the Hamiltonian of the system leading, after Legendre's transformation, to a non covariant Lagrangian which is in contradiction with one of the main principles of General Relativity. A more consistent way to deal with the big rip singularity avoidance is to disregard modification in the gravitational part of the Hamiltonian, and only consider inverse volume effects [2]. In this case we will see that, not like the big bang singularity, the big rip singularity survives in loop quantum cosmology. Another way to deal with the big rip avoidance is to take into account geometric quantum effects given by the the Wheeler-De Witt equation. In that case, even though the wave packets spread, the expectation values satisfy the same equations as their classical analogues. Then, following the viewpoint adopted in loop quantum cosmology, one can conclude that the big rip singularity survives when one takes into account these quantum effects. However, the spreading of the wave packets prevents the recover of the semiclassical time, and thus, one might conclude that the classical evolution of the universe come to and end before the big rip is reached. This is not conclusive because. as we will see, it always exists other external times that allows us to define the classical and quantum evolution of the universe up to the big rip singularity.},

doi = {10.1088/1475-7516/2012/11/037},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 11,

volume = 2012,

place = {United States},

year = {Thu Nov 01 00:00:00 EDT 2012},

month = {Thu Nov 01 00:00:00 EDT 2012}

}