# NEC violation in mimetic cosmology revisited

## Abstract

In the context of Einstein gravity, if the null energy condition (NEC) is satisfied, the energy density in expanding space–times always decreases while in contracting space–times the energy density grows and the universe eventually collapses into a singularity. In particular, no non-singular bounce is possible. It is, though, an open question if this energy condition can be violated in a controlled way, *i.e.*, without introducing pathologies, such as unstable negative-energy states or an imaginary speed of sound. In this letter, we will re-examine the claim that the recently proposed mimetic scenario can violate the NEC without pathologies. We show that mimetic cosmology is prone to gradient instabilities even in cases when the NEC is satisfied (except for trivial examples). Most interestingly, the source of the instability is always the Einstein–Hilbert term in the action. The matter stress-energy component does not contribute spatial gradient terms but instead makes the problematic curvature modes dynamical. Finally, we also show that mimetic cosmology can be understood as a singular limit of known, well-behaved theories involving higher-derivative kinetic terms and discuss ways of removing the instability.

- Authors:

- Princeton Univ., Princeton, NJ (United States)

- Publication Date:

- Research Org.:
- The Trustees of Princeton Univ., Princeton, NJ (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1259571

- Alternate Identifier(s):
- OSTI ID: 1362023

- Grant/Contract Number:
- FG02-91ER40671

- Resource Type:
- Journal Article: Published Article

- Journal Name:
- Physics Letters. Section B

- Additional Journal Information:
- Journal Volume: 760; Journal Issue: C; Journal ID: ISSN 0370-2693

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; null energy condition; non-singular bounce; ghost; gradient instability; mimetic cosmology

### Citation Formats

```
Ijjas, Anna, Ripley, Justin, and Steinhardt, Paul J.
```*NEC violation in mimetic cosmology revisited*. United States: N. p., 2016.
Web. doi:10.1016/j.physletb.2016.06.052.

```
Ijjas, Anna, Ripley, Justin, & Steinhardt, Paul J.
```*NEC violation in mimetic cosmology revisited*. United States. doi:10.1016/j.physletb.2016.06.052.

```
Ijjas, Anna, Ripley, Justin, and Steinhardt, Paul J. Tue .
"NEC violation in mimetic cosmology revisited". United States. doi:10.1016/j.physletb.2016.06.052.
```

```
@article{osti_1259571,
```

title = {NEC violation in mimetic cosmology revisited},

author = {Ijjas, Anna and Ripley, Justin and Steinhardt, Paul J.},

abstractNote = {In the context of Einstein gravity, if the null energy condition (NEC) is satisfied, the energy density in expanding space–times always decreases while in contracting space–times the energy density grows and the universe eventually collapses into a singularity. In particular, no non-singular bounce is possible. It is, though, an open question if this energy condition can be violated in a controlled way, i.e., without introducing pathologies, such as unstable negative-energy states or an imaginary speed of sound. In this letter, we will re-examine the claim that the recently proposed mimetic scenario can violate the NEC without pathologies. We show that mimetic cosmology is prone to gradient instabilities even in cases when the NEC is satisfied (except for trivial examples). Most interestingly, the source of the instability is always the Einstein–Hilbert term in the action. The matter stress-energy component does not contribute spatial gradient terms but instead makes the problematic curvature modes dynamical. Finally, we also show that mimetic cosmology can be understood as a singular limit of known, well-behaved theories involving higher-derivative kinetic terms and discuss ways of removing the instability.},

doi = {10.1016/j.physletb.2016.06.052},

journal = {Physics Letters. Section B},

number = C,

volume = 760,

place = {United States},

year = {Tue Jun 28 00:00:00 EDT 2016},

month = {Tue Jun 28 00:00:00 EDT 2016}

}

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