# Cosmological constant problem and renormalized vacuum energy density in curved background

## Abstract

The current vacuum energy density observed as dark energy ρ{sub dark}≅ 2.5×10{sup −47} GeV{sup 4} is unacceptably small compared with any other scales. Therefore, we encounter serious fine-tuning problem and theoretical difficulty to derive the dark energy. However, the theoretically attractive scenario has been proposed and discussed in literature: in terms of the renormalization-group (RG) running of the cosmological constant, the vacuum energy density can be expressed as ρ{sub vacuum}≅ m {sup 2} H {sup 2} where m is the mass of the scalar field and rather dynamical in curved spacetime. However, there has been no rigorous proof to derive this expression and there are some criticisms about the physical interpretation of the RG running cosmological constant. In the present paper, we revisit the RG running effects of the cosmological constant and investigate the renormalized vacuum energy density in curved spacetime. We demonstrate that the vacuum energy density described by ρ{sub vacuum}≅ m {sup 2} H {sup 2} appears as quantum effects of the curved background rather than the running effects of cosmological constant. Comparing to cosmological observational data, we obtain an upper bound on the mass of the scalar fields to be smaller than the Planck mass, m ∼<more »

- Authors:

- Theory Center, IPNS, KEK, Tsukuba 305-0801, Ibaraki (Japan)
- The Graduate University of Advanced Studies (Sokendai), Tsukuba 305-0801, Ibaraki (Japan)

- Publication Date:

- OSTI Identifier:
- 22676182

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 06; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COMPARATIVE EVALUATIONS; COSMOLOGICAL CONSTANT; ENERGY DENSITY; GEV RANGE; MASS; NONLUMINOUS MATTER; RENORMALIZATION; SCALAR FIELDS; SPACE-TIME

### Citation Formats

```
Kohri, Kazunori, and Matsui, Hiroki, E-mail: kohri@post.kek.jp, E-mail: matshiro@post.kek.jp.
```*Cosmological constant problem and renormalized vacuum energy density in curved background*. United States: N. p., 2017.
Web. doi:10.1088/1475-7516/2017/06/006.

```
Kohri, Kazunori, & Matsui, Hiroki, E-mail: kohri@post.kek.jp, E-mail: matshiro@post.kek.jp.
```*Cosmological constant problem and renormalized vacuum energy density in curved background*. United States. doi:10.1088/1475-7516/2017/06/006.

```
Kohri, Kazunori, and Matsui, Hiroki, E-mail: kohri@post.kek.jp, E-mail: matshiro@post.kek.jp. Thu .
"Cosmological constant problem and renormalized vacuum energy density in curved background". United States.
doi:10.1088/1475-7516/2017/06/006.
```

```
@article{osti_22676182,
```

title = {Cosmological constant problem and renormalized vacuum energy density in curved background},

author = {Kohri, Kazunori and Matsui, Hiroki, E-mail: kohri@post.kek.jp, E-mail: matshiro@post.kek.jp},

abstractNote = {The current vacuum energy density observed as dark energy ρ{sub dark}≅ 2.5×10{sup −47} GeV{sup 4} is unacceptably small compared with any other scales. Therefore, we encounter serious fine-tuning problem and theoretical difficulty to derive the dark energy. However, the theoretically attractive scenario has been proposed and discussed in literature: in terms of the renormalization-group (RG) running of the cosmological constant, the vacuum energy density can be expressed as ρ{sub vacuum}≅ m {sup 2} H {sup 2} where m is the mass of the scalar field and rather dynamical in curved spacetime. However, there has been no rigorous proof to derive this expression and there are some criticisms about the physical interpretation of the RG running cosmological constant. In the present paper, we revisit the RG running effects of the cosmological constant and investigate the renormalized vacuum energy density in curved spacetime. We demonstrate that the vacuum energy density described by ρ{sub vacuum}≅ m {sup 2} H {sup 2} appears as quantum effects of the curved background rather than the running effects of cosmological constant. Comparing to cosmological observational data, we obtain an upper bound on the mass of the scalar fields to be smaller than the Planck mass, m ∼< M {sub Pl}.},

doi = {10.1088/1475-7516/2017/06/006},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 06,

volume = 2017,

place = {United States},

year = {Thu Jun 01 00:00:00 EDT 2017},

month = {Thu Jun 01 00:00:00 EDT 2017}

}