The Cosmological Constant and a Scalar Field Coupled non Minimally to Gravity


We show that the combined minimal and non minimal interaction with the gravitational field may produce the generation of a cosmological constant without self-interaction of the scalar field. In the same vein we analyze the existence of states of a scalar field that by a combined interaction of minimal and non minimal coupling with the gravitational field can exhibit an unexpected property, to wit, they are acted on by the gravitational field but do not generate gravitational field. In other words, states that seems to violate the action-reaction principle. We present explicit examples of this situation in the framework of a spatially isotropic and homogeneous universe.

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  1. 1.

    We note that the expression of the constant value of the field reads \( {\varphi}_0^2=4{\theta}_0^2/3{\mu}^2{L}_{Pl}^2 \). In the paper we are using units such that the Planck lenght is equal to 1.

  2. 2.

    Compare with the case of SSB in which the condition to extremize the potential yields the same result for the particular choice of constant λ given by λ = 3bμ2/4.


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We would like to acknowledge the financial support from brazilian agencies Finep, Faperj and CNPq.

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Correspondence to M. Novello.

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Novello, M., Hartmann, A. The Cosmological Constant and a Scalar Field Coupled non Minimally to Gravity. Int J Theor Phys 59, 1–9 (2020).

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  • Non minimal coupling
  • Cosmological constant
  • Expanding universe