... ¹

E-mail address: ansoldi@trieste.infn.it

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... Aurilia²

E-mail address: aaurilia@csupomona.edu

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... ³

E-mail address: spallucci@vstst0.ts.infn.it

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... Smailagic⁴

E-mail address: anais@etfos.hr

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... undefined⁵

Here $p$ stands for the number of world indices, or rank, of the gauge potential, and $d$ represents the number of spacetime dimensions. The metric is Minkowskian and our signature convention is $(\, -\,+\,+\,+\,\dots\, +\,)$.

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... empty⁶

In a Riemannian spacetime, with non zero curvature, that arbitrary constant cannot be set, in general, equal to zero, and plays the physical role of a ``cosmological constant'' [4]. As a matter of fact, the role of that constant is of paramount importance in most models of cosmic inflation [5].

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... form⁷

In the following discussion we have suppressed all indices in order to simplify the notation. Thus, the Hodge dual of a $(p+1)$-form, including the appropriate combinatorial factor, is simply indicated by $F^{\,*}\equiv {1\over (p+1)!} \epsilon^{\mu_1\dots\mu_{d-p-1}\dots\mu_d} \, F_{\mu_{d-p-1}\dots\mu_d}$, while the product of two $p$-forms becomes: $A\, B\equiv {1\over p!}\,A_{\mu_1\dots \mu_p}\, B^{\mu_1\dots \mu_p}$.

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... zero-form⁸

We have chosen the symbol $J^*$ for the zero-form to order to match the notation in the parent Lagrangian (19). Note that the same reasoning applies to the `` magnetic '' current $K$ in the absence of an `` electric '' current $J$.

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