Unified Dark Matter and Dark Energy in a model of Non-Canonical Scalar-Tensor Theory
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| Format: | Preprint |
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2025
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| _version_ | 1866914108759080960 |
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| author | Pullisseri, Nihal Jalal Unnikrishnan, Sanil |
| author_facet | Pullisseri, Nihal Jalal Unnikrishnan, Sanil |
| contents | We consider a model of non-canonical scalar-tensor theory in which the kinetic term in the Brans-Dicke action is replaced by a non-canonical scalar field Lagrangian $\mathcal{L}(X, ϕ)= λX^αϕ^β- V(ϕ)$ where $X = (1/2) \partial_μ ϕ\partial^μ ϕ$ and $α$, $β$ and $λ$ are parameters of the model. This can be considered as a simple non-canonical generalization of the Brans-Dicke theory with a potential term which corresponds to a special case of this model with the values of the parameter $α= 1$, $β= -1$ and $λ= 2w_{_{BD}}$ where $w_{_{BD}}$ is the Brans-Dicke parameter. Considering a spatially flat Friedmann-Robertson-Walker Universe with scale factor $a(t)$, it is shown that, in the matter free Universe, the kinetic term $λX^αϕ^β$ can lead to a power law solution $a(t)\propto t^{n}$ but the maximum possible value of $n$ turns out to be $(1+\sqrt{3})/4 \approx 0.683$. When $α\geq 18$, this model can lead to a solution $a(t)\propto t^{2/3}$, thereby mimicking the evolution of scale factor in a cold dark matter dominated epoch with Einstein's General Relativity (GR). With the addition of a linear potential term $V(ϕ) = V_{0}ϕ$, it is shown that this model mimics the standard $Λ$CDM model type evolution of the Universe. The larger the value of $α$, the closer the evolution of $a(t)$ in this model to that in the $Λ$CDM model based on Einstein's GR. The purpose of this paper is to demonstrate that this model with a linear potential can mimic the GR based $Λ$CDM model. However, with an appropriate choice of the potential $V(ϕ)$, this model can provide a unified description of both dark matter and dynamical dark energy, as if it were based on Einstein's GR. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_07103 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unified Dark Matter and Dark Energy in a model of Non-Canonical Scalar-Tensor Theory Pullisseri, Nihal Jalal Unnikrishnan, Sanil General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics We consider a model of non-canonical scalar-tensor theory in which the kinetic term in the Brans-Dicke action is replaced by a non-canonical scalar field Lagrangian $\mathcal{L}(X, ϕ)= λX^αϕ^β- V(ϕ)$ where $X = (1/2) \partial_μ ϕ\partial^μ ϕ$ and $α$, $β$ and $λ$ are parameters of the model. This can be considered as a simple non-canonical generalization of the Brans-Dicke theory with a potential term which corresponds to a special case of this model with the values of the parameter $α= 1$, $β= -1$ and $λ= 2w_{_{BD}}$ where $w_{_{BD}}$ is the Brans-Dicke parameter. Considering a spatially flat Friedmann-Robertson-Walker Universe with scale factor $a(t)$, it is shown that, in the matter free Universe, the kinetic term $λX^αϕ^β$ can lead to a power law solution $a(t)\propto t^{n}$ but the maximum possible value of $n$ turns out to be $(1+\sqrt{3})/4 \approx 0.683$. When $α\geq 18$, this model can lead to a solution $a(t)\propto t^{2/3}$, thereby mimicking the evolution of scale factor in a cold dark matter dominated epoch with Einstein's General Relativity (GR). With the addition of a linear potential term $V(ϕ) = V_{0}ϕ$, it is shown that this model mimics the standard $Λ$CDM model type evolution of the Universe. The larger the value of $α$, the closer the evolution of $a(t)$ in this model to that in the $Λ$CDM model based on Einstein's GR. The purpose of this paper is to demonstrate that this model with a linear potential can mimic the GR based $Λ$CDM model. However, with an appropriate choice of the potential $V(ϕ)$, this model can provide a unified description of both dark matter and dynamical dark energy, as if it were based on Einstein's GR. |
| title | Unified Dark Matter and Dark Energy in a model of Non-Canonical Scalar-Tensor Theory |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2510.07103 |